Adsorption Behaviors of Different Water Structures on the Fluorapatite (001) Surface: A DFT Study

To investigate the effect of hydration behavior on the fluorapatite structure, single H2O molecule and three-layer water cluster adsorptions on the fluorapatite (001) surface were performed by means of density functional theory. The results show that a single H2O molecule can form stable chemisorption structures with the fluorapatite (001) surface in the form of single-site, two-site, and three-site adsorption and that the corresponding adsorption energies are 64.817, 98.712, and 139.620 kJ/mol, respectively. The interacting length of the Ca atom and the O atom of the H2O molecule is close to the length of the Ca–O bond in the bulk, and their overlap is mainly contributed by the O 2p and Ca 4s states. The fluorapatite (001) surface shows serious hydration reconstruction after adsorbing three layers of water molecules; these atoms in the surface layer are highly distorted, and the Ca and the PO4 are shifted in opposite directions along the z-axis direction. Further analysis shows that these surface Ca atoms are critical to the hydration behaviors of the transition area, as they can bind strongly to the H2O molecules, with the newly formed Ca–O bonds being between 2.164 and 2.486 Å.


INTRODUCTION
Apatites have attracted more and more attention due to their complex structures and unique properties. On the one hand, because they are the most important bone material, the study of apatites occupies a huge market in the field of life science (Palazzo et al., 2007;Rey et al., 2014;Okada and Matsumoto, 2015); on the other hand, there are many valuable elements in them, such as rare earths, uranium, and thorium, which play significant roles in the development of future energy, high-end equipment, and other advancements of various key technologies (Li et al., 2014;Zhang, 2014;Emsbo et al., 2015). However, we should not ignore the fact that apatites, and mostly fluorapatite, are the main phosphorus-bearing minerals and play an irreplaceable role in industrial and agricultural production (Scholz et al., 2014). Data reveals that more than 90% of the fluorapatite resource is used to produce fertilizer, with other applications being in animal feed, detergents, food and beverages, and water treatment (Rawashdeh and Maxwell, 2011). Not all phosphate ores can be used directly, and this is becoming more and more of an issue as rich fluorapatite resources become even scarcer. With the further depletion of the apatite resources, billions of tons of apatite ores need to be pretreated by flotation. It is reported that more than half of the world's marketable phosphate is concentrated via the flotation process, which takes place at the complex solid, water, and gas phase interface (Santos et al., 2010).
The existence of a water environment is a necessity for flotation, and the hydration behavior of the surface is very important. However, corresponding research is still needed, and progress has been slow. Due to the development of modern microscopic detection equipment, this trend has improved dramatically. Park et al. (2005) studied the structure of the Durango fluorapatite (100)-water interface with high-resolution X-ray reflectivity and found that the presence of a layered interfacial water structure exhibits two distinct water layers and that the heights of the first and second layers are 2.64 and 4.17 Å, respectively. Dan et al. (2006) conducted research on calcium surface sites at aqueous fluorapatite by means of 1 H and 31 P MAS NMR. Meanwhile, Pareek et al. (2008Pareek et al. ( , 2009) made a systematic study of the role of water in the surface relaxation of the fluorapatite (100) surface with grazing incidence x-ray diffraction. In recent years, with the continuous progress of computer technology, the density functional theory method (DFT), which can be used to describe collector-mineral adsorption at the molecular level in 3D space, has triggered intense research and is providing valuable primary information on various interface systems (Mkhonto and de Leeuw, 2002;Rulis et al., 2004Rulis et al., , 2007Haverty et al., 2005;Chappell et al., 2008;Menéndez-Proupin et al., 2011). Mkhonto and de Leeuw (2002) studied the effect of water on the surface structure and morphology of fluorapatite and found that the hydration of the surfaces occurs by physisorption and shows Langmuir behavior. Mkhonto and de Leeuw (2002) studied the interaction of (001) carbonated hydroxylapatite surfaces with water. They found that a single molecule of water can be strongly adsorbed by the apatite surface and that the carbonate ion may lower both the adsorbate/surface interaction energy and the energy needed to deform the COHAp surface and the water molecule. However, many questions relating to the details of water adsorption on the fluorapatite surface at the molecular level remain without clear answers.
In this paper, the fluorapatite (001) surface was chosen to investigate the interactions between the fluorapatite (001) surface and single H 2 O molecule as well as water cluster, respectively. Different configurations were optimized, and the mechanism of water adsorptions on the fluorapatite (001) surface and their influence are discussed. The results provide an important insight into the structure of and enable investigation of flotation reagent interactions on the fluorapatite surface, which may aid current experimental efforts to understand the flotation process further.

Computational Methods
Calculations for the fluorapatite (001) surface and single H 2 O molecule adsorptions were performed within Cambridge Serial Total Energy Package (CASTEP) (Clark et al., 2005). For the former calculations, the ultrasoft pseudo-potential was employed to describe the electron-ion interactions. The exchange correlation function used in the present study was the generalized gradient approximation (GGA), which was extended by the Perdew-Wang generalized-gradient approximation (PW91). The plane-wave cutoff of 400 eV was chosen, and the Brillouin zone was sampled with k-points of a 2 × 2 × 2 grid, which were found to be enough for the system. The convergence tolerances were set as follows: the maximum displacement was 0.002 Å, the maximum force was 0.08 eV·Å −1 , the maximum energy change was 2.0 × 10 −5 eV·atom −1 , the maximum stress was 0.1 GPa, and the SCF convergence tolerance was 2.0 × 10 −6 eV·atom −1 . The valence electron configurations considered in all the studies were H 1s 1 , O 2s 2 2p 4 , F 2s 2 2p 5 , P 3s 2 3p 3 , Ca 3s 2 3p 6 4s 2 .

Computational Models
The bulk crystal structure of the fluorapatite was obtained from the American Mineralogist Crystal Structure Database (AMCSD). The lattice parameters were calculated as a = b = 9.457 Å and c = 6.883 Å, which were in good agreement with the experimental results (a = b = 9.375 Å and c = 6.887 Å) (Comodi et al., 2001). As shown in Figure 1, each fluorapatite bulk possesses two Ca 5 (PO 4 ) 3 F structures along the (001) plane, with the stacking sequence of Ca-Ca 3 (PO 4 ) 3 F-Ca-Ca-Ca 3 (PO 4 ) 3 F-Ca. These adjacent Ca-1 and Ca-2 sites are rather different in that the columnar Ca-1 site is coordinated to nine oxygen atoms in the arrangement of a tricapped trigonal prism, while the mirror Ca-2 site is in the Ca 3 (PO 4 ) 3 F layer and bonds to six oxygen atoms and the column anion F (Hughes and Rakovan, 2002). However, the oxygen atoms are not very different, and they are marked for the sake of data discussion. The most stable surface was chosen, though there are different kinds of terminations along the (001) plane (Qiu et al., 2017). After testing, the (22) fluorapatite (001) surface structure with fifteen atomic layers was constructed, and the five bottom-most atomic layers were fixed to the bulk (see Figure 2). The vacuum gap of 30 Å in the z-direction was sufficient for our investigation.
The optimization of a single H 2 O molecule was performed in a 10 × 10 × 10Å cubic cell, and the calculated results (see Figure 3A) are close to the experimental observations (Zhao et al., 2014;Chen et al., 2017). Adsorption clusters of three layers of water molecules (see Figure 3B) were optimized with the same condition, which was used to simulate the natural state of water.
The adsorption energy of H 2 O on the fluorapatite surface is calculated by the following equation (Zhao et al., 2015):

Adsorption of a Single H 2 O Molecule on the Fluorapatite (001) Surface
As shown in Figure 2, the exposed atoms of the fluorapatite (001) surface can be divided into three parts. The Ca-1 atoms occupy the first layer, and the other atoms in the second layer can be divided into two parts, the O-1 atom in the first sublayer and Ca-2, P, O-2, and O-3 atoms in the second sublayer. So from top to bottom are Ca-1 atoms, O-1 atoms, and then Ca-2, P, O-2, Frontiers in Materials | www.frontiersin.org and O-3 atoms. Usually, the tetrahedral PO 4 -group is considered indivisible in reactions, so the potential centers are divided into four parts, Ca-1, Ca-2, PO 4 -group, and F sites. It is worth noting that the F and Ca-2 atoms are not as active as other atoms, such as Ca-1 and O atoms, during the single H 2 O molecule adsorption; the optimized stable configurations are shown in Figure 4. As seen in Figure 4A, the length between O 73 and Ca 6 is 2.317 Å, which is close to that of the Ca-O bond in the bulk. Meanwhile, the calculated E ads is −64.817 kJ/mol, confirming that the interaction between the Ca and O atoms is rather strong. As shown in Table 1, the O 73 atom exhibits the ability to gain electrons, and its 2p state increases from 5.13 to 5.16e, while the Ca 6 atom shows some electron-donating behavior and the main electron loss orbital is its 4s state (from 2.20 to 2.12e). The configuration of the H 2 O molecule changes very little, which suggests that this kind of adsorption is insufficient to initiate the decomposition of the H 2 O molecule.
For further study, DOS analysis of the single-site H 2 O adsorption on the fluorapatite (001) surface is presented. As revealed in Figure 5, the DOS of the H 2 O molecule has a distinct shift to the lower energy area after absorbing on the (001) surface of fluorapatite. For the Ca 6 , the peak in the conduction band contributed by the 3s state has been greatly weakened. Significant overlap is seen in the range from 2 to 3.5 eV, which is contributed by the O 2p and Ca 3s states. In addition, some bonding interactions also can be observed in the range from −8 to −4eV and 2 to 3eV. Figure 4B shows the double-site adsorption configuration of the H 2 O molecule on the fluorapatite (001) surface. It is found that strong bonding interaction exists between O 73 and Ca 6 , with a distance of 2.327 Å (see Table 2     As seen in Figure 6, the DOS of the H 2 O molecule has the same distinct shift to the left and the structure changes greatly, with the valence bands mixing together from −6.51 to 0.05 eV, indicating strong charge transfer during the adsorption process. The apparent change for the Ca 6 is these peaks in the conduction band, which are contributed by 3p and 3d states. For the O 54 , all of the bands move to the lower energy area. Meanwhile, the parts near the Fermi level contributed by the 2p state broaden, but the peak next to the Fermi level shows a decrease from 2.5 to 2 eV. The potential bonding interactions both for the H 2 O-Ca 6 and H 2 O-O 54 systems are distributed near the top of the valence band.
As shown in Figure 4C, the length of O 73 and Ca 12 , Ca 27 is 2.473 Å and 2.761 Å, and the obvious hydrogen bond of H 2 and O 52 is 1.622 Å. Our calculated result shows that the E ads is as large as −139.620 kJ/mol, which indicates that this configuration is very stable. It is seen in Figure 7 that the DOS of the H 2 O molecule has a distinct shift to the left, and the structure change greatly too, which indicates a strong charge transfer during the adsorption process. The obvious change of the Ca 21 is that its peak at 2.7 eV contributed by the 4s state is weakened. For the Ca 27 , its valence band, which is contributed by the 3p state, is broadened, and the peak at 20.5 eV is weakened from 7.32 to 5386 eV. The top valence band of the O 52 , which is contributed by its 2p state, becomes wider and moves away from the Fermi level, which may affect its chemical properties. Meanwhile, the peak next to the Fermi level drops to 0.75 eV.

Adsorption Configurations of a Water Cluster on the Fluorapatite (001) Surface
The adsorption configuration of three layers of water molecules on the fluorapatite (001) surface was optimized and is shown in Figure 8. It is an interesting phenomenon that a transitional interfacial layer is formed containing water molecules and Ca atoms, which suggests that strong hydration occurs in this  region and that the fluorapatite (001) surface undergoes a drastic reconstitution. The whole area can be divided into four parts: the upmost layer is near-free water, the second is a tight adsorption layer, the third is a chaotic adsorption layer, and finally, the fourth layer is the mineral structure. Table 4 shows the atomic displacement of the fluorapatite (001) surface. The calculation formula (Cui and Liu, 2010) is as follows: Here, d i represents the relative atomic coordinate shift of O, P, Ca, and F atoms; d before is the corresponding pre-adsorption atomic coordinate; d after represents the coordinate after adsorption; a refers to the bulk lattice parameter along the x-axis before geometry optimization.
The relative atomic displacements of the fluorapatite (001) surface are presented in Table 4. It is found that the Ca-1 sites in the first layer have the largest distorted displacements and  that the corresponding movements along the x-, y-, and z-axis directions are −16.961% ∼ 7.427%, −9.188% ∼ 5.285%, and 5.273% ∼ 20.042%. The Ca-2 sites in the second layer possess the second-largest distorted displacements, and the main movement is −3.046% ∼ 14.153% in the z-axis direction. The PO 4 group moves toward the vacuum region strongly in the negative z-axis direction, which is in the opposite direction from the previous two Ca sites. The Ca-1 sites in both the third and fourth layers are quite stable, and their displacements along the z-axis direction are about 3 and 1%, respectively. As shown in Figure 8, the displacement of the PO 4 group seems not to be large; however, the Ca-1 atoms have entered the water environment, and the Ca-2 atoms also show significant upward displacement, which means that the fluorapatite (001) surface is severely dissociated. This result can well explain the source of Ca 2+ in slurry. However, we have noted that some experimental reports on the adsorption behavior on the fluorapatite (100) surface (Park et al., 2005;Pareek et al., 2007Pareek et al., , 2008) seem a little different from our calculations, though the adsorption behaviors of the two surfaces are not much different. This discrepancy may be attributable to the dissolution of sensitive Ca-1 atoms during sample preparation. As shown in Table 5, if we take away the chaotic adsorption layer, then the result will be very close to the experimental value.
The bindings of the mineral structure and the chaotic adsorption layer are mainly contributed by the Ca-2 atoms with the Ca-O ionic bond. Each Ca atom is bonded to six O atoms, half of which come from the H 2 O molecule, and the length of these newly formed bonds is 2.215∼ 2.439 Å. In addition, a few weak hydrogen bond interactions can be seen, which are contributed by the O atoms from PO 4 groups and the H atoms from H 2 O molecules; their length is between 2.164 and 2.472 Å. The interactions in the chaotic adsorption layer are mainly due to the Ca-O ionic bond and the hydrogen bond; the latter comes from the H 2 O molecule. Each Ca is surrounded by six H 2 O molecules, which usually contain three molecules from the tight sorption layer. The lengths of the Ca-O bond and hydrogen bond are between 2.237 and 2.486 Å and from 1.903 to 1.956 Å, respectively. The lengths of the hydrogen bonds of the tight adsorption layer and free water layer are not much different and are basically between 1.913 and 1.967 Å; however, the lengths of the interlaminar hydrogen bonds of the latter are slightly greater than those of the former.

CONCLUSION
To investigate the effect of hydration behavior on the structure of fluorapatite, single H 2 O molecule and three-layer cluster adsorptions on the fluorapatite (001) surface were performed by means of density functional theory. The conclusions can be summarized as follows: (

DATA AVAILABILITY STATEMENT
The datasets generated for this study are available on request to the corresponding authors.