Density Functional Theory Study of Interface Interactions in

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A Density Functional Theory Study of Interface Interactions in Hydroxyapatite / Rutile Composites for Biomedical Applications Irina Yu. Grubova, Maria A. Surmeneva, Stijn Huygh, Roman A. Surmenev, and Erik Cornelis Neyts J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b02926 • Publication Date (Web): 27 Jun 2017 Downloaded from http://pubs.acs.org on July 5, 2017

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The Journal of Physical Chemistry

A Density Functional Theory Study of Interface Interactions in Hydroxyapatite / Rutile Composites for Biomedical Applications Irina Yu. Grubovaa,b, Maria A. Surmenevaa, Stijn Huyghb, Roman A. Surmeneva,*, Erik C. Neytsb,* a

Department of Experimental Physics, National Research Tomsk Polytechnic University,

Lenin Avenue, 30, 634050 Tomsk, Russia b

Department of Chemistry, PLASMANT Research Group, University of Antwerp,

Universiteitsplein 1, B-2610 Wilrijk-Antwerp, Belgium *Corresponding authors: Tel.: +79039530969 (Tomsk), Tel.: +3232652388 (Antwerp) E-mail address: [email protected] (R. Surmenev), [email protected] (E. Neyts)

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Abstract To gain insight into the nature of the adhesion mechanism between hydroxyapatite (HA) and rutile (rTiO2), the mutual affinity between their surfaces was systematically studied using density functional theory (DFT). We calculated both bulk and surface properties of HA and rTiO2, and explored the interfacial bonding mechanism of amorphous HA (aHA) surface onto amorphous as well as stoichiometric and non-stoichiometric crystalline rTiO2. Formation energies of bridging and sub-bridging oxygen vacancies considered in the rTiO2 (110) surface were evaluated and compared with other theoretical and experimental results. The interfacial interaction was evaluated through the work of adhesion. For the aHA / rTiO2 (110) interfaces, the work of adhesion is found to depend strongly on the chemical environment of the rTiO2 (110) surface. Electronic analysis indicates that the charge transfer is very small in the case of interface formation between aHA and crystalline rTiO2 (110). In contrast, significant charge transfer occurs between aHA and amorphous rTiO2 (aTiO2) slabs during the formation of the interface. Charge density difference (CDD) analysis indicates that the dominant interactions in the interface have significant covalent character, and in particular the Ti-O and Ca-O bonds. Thus, the obtained results reveal that the aHA / aTiO2 interface shows a more preferable interaction and is thermodynamically more stable than other interfaces. These results are particularly important for improving the long-term stability of HA-based implants.

Introduction Hydroxyapatite [Ca10(PO4)6(OH)2, HA] ceramics, known for its bioactive nature, is the most stable calcium phosphate (CaP) mineral in the human body.1 It is often applied as a coating on a metallic substrate for enhancing the bone formation process around an implant.2 The most commonly used substrates for HA coating deposition are titanium (Ti) and its 2 ACS Paragon Plus Environment

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alloys, which are clinically used as metal implants due to their good mechanical properties and high corrosion resistance.3-5 HA-coated Ti alloy biocomposite implants show excellent biocompatibility and satisfactory mechanical properties during short-term implant-to-bone fixation.3,6 However, a drawback of this coating/substrate system is its poor adhesion at the interface, which limits the long-term performance of the implants by its influence on the mechanical, anticorrosive, and tribological characteristics as well as its integrity. There are some commonly accepted guidelines for enhancing the adhesion at the HA / Ti interface7, including a denser microstructure and thinner HA coatings resulting in high bonding strength8,9, reducing the residual stress10, doping HA with other elements such as Si, Sr, and Ag8,11-12, controlling the Ti substrate surface texture and compositions13,14, and controlling the choice of deposition method and its operating conditions.6,15-16 Although a large number of experimental studies have already been carried out and provided valuable results, the nature and the mechanism of the HA interaction with Ti at the coating / substrate interface is still far from being fully understood. Thus, the complexity of the interactions at the HA / Ti interface encouraged us to investigate this phenomenon with a detailed theoretical analysis using density functional theory (DFT), which can help to understand the interactions at the atomic and molecular level, and which cannot be investigated directly through experiments. Although modeling oxide/oxide and oxide/metal interfaces with DFT has been very successful17-21, most of such studies investigate only a rather limited range of the surface compositions. Moreover, only little detailed interface characterization data is available for HA’s crystal structure due to its complexity. The bulk structure of HA, on the other hand, is well-established via simulation studies.22-24 The agreement between HA properties calculated with DFT and experimentally obtained bulk properties of HA suggests that this method could allow us to describe the surface properties in vacuum reasonably well.22



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It is known that Ti typically forms a thin (1.5−25 nm) overlayer of titanium dioxide (TiO2), whose dominant phases are rutile (rTiO2) with its most stable surface orientations (110) or (100) and anatase with (101) or (001) surfaces, respectively.25 The (110) surface of rTiO2 is particularly attractive for the investigation of its interactions at the HA / Ti interface since it is the lowest energy surface and therefore plays the greatest role in determining the surface chemistry. In this contribution, we employ DFT calculations to investigate the interaction (work of adhesion and interface energy) between aHA and various types of rTiO2 slabs. We study the interaction between aHA and amorphous TiO2 (aTiO2) structures, because the native oxide that spontaneously forms on the Ti surface in ambient air is amorphous and experimental data have shown that HA at the interface also has an amorphous structure.26 The rest of paper is organized as follows. First, theoretical results for the bulk materials (HA and rTiO2) will be reported. Subsequently, the atomic-scale interaction at the aHA / crystalline rTiO2 (110) interface with and without vacancies and aTiO2 are investigated. Finally, a summary and conclusion is given.

Calculation Method We employ DFT calculations as implemented in the VASP (Vienna ad initio Simulation Package) code.27-31 The exchange–correlation interactions are treated at the GGA level, employing the Perdew–Burke–Ernzerhof (PBE) functional32,33 using plane wave basis sets and the projector-augmented wave method as implemented in VASP.31,34 The included valence electrons are 1s1 for hydrogen, 3s23p3 for phosphorus, 3s23p64s2 for calcium, 2s22p4 for oxygen, and 3d34s1 for Ti. A plane-wave cutoff of 600 eV is used in all calculations containing HA, while for the pure rTiO2 cell calculations the energy cutoff was set to 500 eV. The Brillouin zone sampling is done using a 4 × 4 × 4 and 8 × 8 × 8 Monkhorst-Pack k-point


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mesh35 for the HA and rTiO2 bulk calculations, respectively. A 2 × 2 × 1 Γ-centered k-point grid is used in the relaxation of the HA (001) and rTiO2 (110) surfaces, and of the aHA / rTiO2 interfaces, while 6 × 6 × 1 grids are used for the final energy calculation. The total energy is converged to within 0.01 eV. Amorphization of HA is performed using the serial version of ReaxFF,36,37 employing a force field combining the phosphate force field parameters from ref. 38 with the Ca/O/H parameters of ref. 39. A recently developed parametrization for Ti/O40 is used for the amorphization of TiO2 surface. The atomic structures are visualized by VESTA 341.

Results and Discussion Bulk Materials In the present work, we employ the hexagonal form of HA which contains two Ca5(PO4)3OH formula units per unit cell (44 atoms), belonging to space group P63/m, with a=b=9.4239 Å and c=6.8841 Å.42 The hexagonal HA phase is the most frequently encountered experimentally and involved in bone formation, because it allows for easy exchange of OH groups with other anions. The 10 calcium ions are distributed between two nonequivalent crystallographic sites. Six CaII (6h) ions are symmetrically located about the 6fold screw axis and the other four CaI (4f) ions are positioned along the 3-fold axes. Surrounding the CaI ions there are three oxygen triangles, of which one is located above and one is located below the CaI ion, and the third (larger) triangle is almost at the same height along the c-axis as CaI. The larger OH ions are displaced along the z direction because these ions cannot fit within the CaII triangle.43 During the simulations, the symmetry was reduced to the P63 space group by removing two of the OH groups and placing the other two along the c axis, without mirror symmetry, to avoid the mutual overlap of the two partially occupied (OH−) sites (Figure 1a).24 5 ACS Paragon Plus Environment


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(a)

(b)

Figure 1. Schematic representation of the HA (a) and rTiO2 (b) unit cells (Ti-orange; Cablue; O-red, P-purple, H-white). The optimized lattice parameters of the HA unit cell are listed in Table 1 together with experimental values42 and another theoretical estimation.22 The Table shows that our results are in good agreement with the experiment and other DFT calculations, with a discrepancy less than 0.7% with respect to earlier calculations and 3.5% with respect to experimental values. Table 1. Calculated lattice parameters of HA bulk and rTiO2 bulk. Comparison of obtained data with DFT calculations and experimental values.

Present work Calculateda Experimentb Present work Calculatedc Experimentd a Ref 22 b Ref 42 c Ref 44 d Ref 45

System

a=b, Å

c, Å

c/a

V, Å3

HA

9.557 9.580 9.418 4.652 4.642 4.587

6.919 6.930 6.875 2.966 2.973 2.954

0.724 0.724 0.730 0.638 0.640 0.644

547.25 551.20 528.10 64.20 64.10 61.90

rTiO2

It is well known that the rTiO2 primitive cell contains two TiO2 units (15 atoms) (Figure 1b). The calculated bulk lattice parameters for rTiO2 also matched well with reported experimental46 and theoretical results46 (with a discrepancy less than 3.6 % and 0.2 %, respectively).


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HA (001) and rTiO2 (110) Faces We first focus on the interface formed between the most stable HA and rTiO2 surfaces: HA (001) / rTiO2 (110).47-49 The HA (001) surface containing 44 atoms was cut from a converged and fully optimized HA unit cell. The amorphization of HA was performed in ReaxFF using existing phosphate ReaxFF parameters. In the case of the HA (001) surface to generate the amorphous HA structure, we let the system evolve at temperatures ranging from zero to 3000 K, well above the experimental melting point of 1923 K.50 The minimization of this structure was subsequently carried out in VASP (Figure 2a). (a)

(b)

(c)

Figure 2. Final relaxed structure of (a) the amorphous HA (obtained from ‘‘melt-andquench’’ of the 44-atom HA system), (b) stoichiometric rTiO2 (110) and (c) amorphous rTiO2 surfaces (obtained from ‘‘melt-and-quench’’ of the 72-atom rTiO2 system), after atomic relaxation using DFT. Red sphere – O, blue – Ca, white – H, violet – P, orange – Ti). The rTiO2 (110) surface is modeled within the slab approach. We use a (1×3) supercell model of rTiO2 (110) of which the bottom two layers were fixed at the bulk positions. A thickness of four layers (nL = 4) is found to be sufficient to converge the surface energy, yielding a surface energy of ~1.005 J m−2, in agreement with earlier studies51-56 (see Supporting Information). Figure 2b schematically represents the rTiO2 (110) slab structure for nL = 4.



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Numerous studies have established the important role of oxygen (Vo) defects in the surface chemistry of TiO2 (110).57,58 For completeness, we calculate the vacancy formation energies for rTiO2 (110) surfaces and present the obtained data in the Supporting Information. The vacancies were created in the first two surface layers. The bottom two layers of the slab were kept frozen in their bulk positions. Two different oxygen vacancies were considered: a vacancy at the bridging (bri = Vo1) oxygen site and a vacancy at the sub-bridging (sbr = Vo3) oxygen site, due to that fact that these type of oxygen vacancies are most likely at rTiO2 (110) surface (see Supporting Information).59 It is known that TiO2 crystallizes in the most thermodynamically stable rTiO2 modification structure at elevated temperatures, the reported temperatures of anatase to rTiO2 transformation vary in the range of 400–1200 °C owing to the use of different techniques used for the determination of transition temperature, initial material properties, and processing methods.60 The TiO2 force field parametrization of ReaxFF was used for the amorphization of the rTiO2 structure.40 The rTiO2 (110) slab with four layers was heated to 3000 K (melting point of TiO2 crystals is 2173 K),61 run for 7.5 ps and quenched to 0 K. Subsequently, random velocities were assigned to the surface atoms corresponding to 500 K, and finally a temperature ramp from 500 K to 300 K is applied for 5 ps. This procedure was repeated three times for each amorphous structure to reduce stress in the surface. The energetically most stable amorphous structures as derived from the rTiO2 (110) surface were selected from the obtained list and then used for the interface model calculations (Figure 2c). To confirm the amorphicity of obtained aHA and aTiO2 systems, structural properties are compared to experimental data and other theoretical results. The analysis of bond length distribution for aTiO2 models shows that the most of Ti-O bond lengths are distributed between 1.63 to 2.30 Å for all three amorphous slabs, whereas


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for c- rTiO2 (110) Ti-O bond lengths are at 1.98 Å. It was seen that the large number of Ti-O bonds get compressed and a few get expanded as compared to crystalline phase of rTiO2. This observation agrees with previously reported experimental data and with theoretical calculations.62- 63 It is known that the determination of the atomic structure of amorphous CaP (ACaP), due to their chemical variability, is a non-trivial task. The majority of available experimental data describe ACaP as wet-precipitated compounds with Ca/P ratio close to ~ 1.5, i.e. amorphous tricalcium phosphate (TCP). As Poster’s cluster has a chemical composition of TCP, it might be located in the atomic structures of HA, TCPs and octacalcium phosphate (OCP).64 However, the structure of a particular amorphous solid can never be determined unambiguously. Therefore, to confirm the appropriate amorphicity of the 44-atom HA systems using “melt-and-quench’’ technique upon the available literature is rather challenging. Quite recently, Wu et al.65 mimicked the preparation of HA ceramics using a slab model with a simulated annealing molecular dynamics (MD) method and found that the surface atoms are reorganized to form a disordered structure different from HA crystal. The quite similar character of disordering as in the surface reconstruction of the HA structures annealed at 2000-2800 K revealed by Wu et al. was observed in our work.65

Interface Model In total, we constructed six interface models (see Table 2). To identify the possible atomic structures of the interfaces, we first scanned the total interaction between the two surfaces using ReaxFF. During the scanning, all atoms were fixed, and the aHA surface scans over the different surfaces of rTiO2 in three directions (x-direction: 10 points (stepsize: 0.066 Å); ydirection: 10 points (stepsize: 0.089 Å); z-direction: 40 points (stepsize: 0.065 Å)). The



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interaction between the aHA surface and the different surfaces of rTiO2 at all scanning points was analyzed and the stacking configurations with minimum total energy for the entire system were selected for a subsequent DFT optimization (Table 2). Table 2. Numbered stacking positions for six interface models (аHA/aTiO2 (1-3); аHA/rTiO2, аHA/rTiO2(Vo1) and аHA/rTiO2(Vo3), where c-rTiO2 denotes crystalline rutile (110) surface, and rTiO2 (Vo1) and rTiO2 (Vo3) denote rutile (110) surface with vacancies bri and sbr, respectively). аHA/rTiO2 Stacking position

1_ c-rTiO2 2_ c-rTiO2 3_ c-rTiO2

аHA/ rTiO2(Vo1) 1_ (Vo1) 2_ (Vo1) 3_ (Vo1)

аHA/ rTiO2(Vo3) 1_ (Vo3) 2_ (Vo3) 3_ (Vo3)

аHA/aTiO2(1)

аHA/aTiO2(2)

аHA/aTiO2(3)

1_ aTiO2(1) 2_ aTiO2(1) 3_ aTiO2(1) 4_ aTiO2(1)



Thus, six interface models were constructed with the different stacking positions of aHA to crystalline rTiO2 (110) and aTiO2 as defined by ReaxFF (Table 2). All interface models were subsequently relaxed in VASP. The real rTiO2 (110) surface has many defects, such as oxygen vacancies and pits.66 A number of theoretical studies have examined the role of oxygen vacancies on rTiO2 (110) surfaces,67-72 and several of them confirm that the presence of O vacancies strongly increases the reactivity of the surface.68,71-72 While the properties of O vacancies on rTiO2 (110) have been investigated extensively, there are no theoretical studies addressing specifically the adsorption of Ca and phosphate ions on reduced rTiO2. However, its adsorption is believed to the first crucial step in the nucleation of HA on the single crystalline substrates. According to theoretical studies the driving force behind Ca2+ adsorption is the electrostatic interaction between the Ca2+ complexes and the negatively charged deprotonated sites present on the surface of rTiO2 (110).73 In recent studies on nucleation, it was detected that the initial step is the


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deposition of Ca2+ ions on the substrate. The next step of this process is the binding of the PO4 molecules with Ca ions, which would be followed by the formation of an ACaP phase.73 (a)

(b)

(c)

(d)

(e)

(f)



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Figure 3. Side view of the three stacking models between aHA and stoichiometric rTiO2 (110) slab (a-b), defected rTiO2 (110) slabs (c-d and e-f, for Vo3 and Vo1, respectively) before (a, c, e) and after (b, d, f) relaxation. The optimized interface structures for the models at the best stacking positions prior to and after relaxation are presented in Figure 3. Characteristic for the aHA / rTiO2 interfaces is the formation of different Ti−O bonds between the Ti from the rTiO2-slab and the O from the PO4 groups in aHA at the interface. The Ca atoms of the aHA slabs also show the formation of a bonding interaction with rTiO2 surfaces at the interfaces. After relaxation, the bottom Ti layers show a zigzag structure in the cases where crystalline rTiO2 is used. Moreover, a strong distortion in the atomic positions occurred in the aHA structure due to its amorphous structure. (a)

(b)

Figure 4. Side view of the stacking model for aTiO2 slab and aHA interface before (a) and after (b) relaxation. In the аHA / aTiO2 (1-3) interfaces, a significant distortion of the atomic positions occurred for the Ti atoms, as well as for the atoms in aHA during the optimization (Figure 4). In аHA / aTiO2 case the same character of the interaction was observed: the main bonding occurs between the O from the PO4 groups in aHA and the Ti from the rTiO2-slab. There is also a slightly weaker bond between O and Ca than between Ti and O.


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The adhesion of aHA to rTiO2 is characterized by the work of adhesion. The work of adhesion is calculated as follows74:

ܹ௔ௗ =

ଵ ே஺

ൣ‫ܧ‬௧௢௧(୧୬୲) − ‫ܧ‬௧௢௧(ୟୌ୅) − ‫ܧ‬௧௢௧(୰୘୧୓ଶ) ൧,

(1)

where ‫ܧ‬௧௢௧(୧୬୲) is the total energy of the interface system in its optimized geometry,

‫ܧ‬௧௢௧(ୟୌ୅) and ‫ܧ‬௧௢௧(୰୘୧୓ଶ) are the total energies for the corresponding isolated subsystems with the same geometry as that of the optimized interface system, and A (A= 58.5471 Å2) represents the interface surface area. The factor N in eq (1) accounts for the presence of one interface (in our case the N = 1, and hence the aHA/rTiO2 interface model contains a single interface). Table 3. Calculated Total Energy, Work of Adhesion and Integral Charge Transfer (from aHA to rTiO2) for the different interface systems of rTiO2 (c-rTiO2, rTiO2(Vo1), rTiO2(Vo3) and aTiO2(1-3)) and aHA depending on the stacking position. System and stacking position

Wad (J/m2)

aHA / c-rTiO2 1_ c-rTiO2 2_ c-rTiO2 3_ c-rTiO2 aHA / rTiO2(Vo1) 1_ rTiO2(Vo1) 2_ rTiO2(Vo1) 3_ rTiO2(Vo1) aHA / rTiO2(Vo3) 1_ rTiO2(Vo1) 2_ rTiO2(Vo1) 3_ rTiO2(Vo1) aHA / aTiO2(1) 1_ aTiO2(1) 2_ aTiO2(1) 3_ aTiO2(1) 4_ aTiO2(1) aHA / aTiO2(2) 1_ aTiO2(2) 2_ aTiO2(2) 3_ aTiO2(2) 4_ aTiO2(2) aHA / aTiO2(3) 1_ aTiO2(3) 2_ aTiO2(3) 3_ aTiO2(3) 4_ aTiO2(3)

Integral charge transfer (ICT) (electron)

-0.106 -0.463 -0.435

-0.132 -0.255 -0.255

-0.582 -0.412 -0.620

-0.161 -0.098 -0.114

-0.251 -0.321 -0.121

-0.250 -0.246 -0.016

-0.957 1.647 1.143 -0.841

-0.227 -1.065 -1.017 -0.482

-0.702 -0.379 -0.018 -1.665

-0.389 -0.660 -1.021 -0.637

-2.060 -0.084 0.055 -2.429

-0.228 -0.968 -1.022 -0.467



Table 3 presents the calculated work of adhesion for 6 interface systems. The more negative the value of the obtained ܹ௔ௗ is, the greater the bonding strength at the interface. It appears from Table 3 that only bri vacancies have an influence on the interfacial adhesion values. Comparison of results obtained for crystalline rTiO2 (110) with or without vacancies and aTiO2 (1-3) reveals that a strong interaction is obtained only for the latter. It should be noted that the precise stacking position also has an influence on the resulting work of adhesion values. Previously, rather similar values of the work of adhesion, in the ranges 0.01 J m−2 and -1.99 J m−2, were obtained for HA(0001) / Ti(0001) interface system using DFT by Sun et al.75

Ca PO4 O (Ti) Ti

10

Density of states (arb. units)

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5

aHA free 0 10

5

Interface 0 10

5

rTiO2(Vo1) free 0 -14

-12

-10

-8

-6

-4

-2

0

2

4

E - Ef (eV)

Figure 5. Partial DOS of optimized aHA / rTiO2(Vo1) interface compared to the free subsystems with the same geometry as that of the interface system. The zero of energy corresponds to the vacuum level. The DOS values for Ca atoms were multiplied by 5.


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Subsequently, we also study the electronic structure of the aHA / rTiO2 interface for better understanding the nature of the interactions. We calculate the total (not shown) and partial densities of states (DOS) for the interface atoms (six Ti atoms, eight oxygen atoms of rTiO2, PO4 moiety, and three Ca atoms) of the most stable model, i.e. aHa / rTiO2(Vo1), as shown in Figure 5. As can be seen in Figure 5, the interaction at the interface leads to significant changes in the DOS at the Fermi level for the aHA, indicating a significant change in the character of the interaction. Although PBE is known to yield inaccurate band gaps, we here focus on the change in electronic structure due to the interface interaction rather than on the precise value of the band gap. We here elaborate on the DOS for the aHA / rTiO2(Vo1) interface as a representative example. The analysis of obtained DOS reveals the presence of a mixed zone in the valence band. It is observed that the p orbital of PO4 unit and d orbital of Ti constitute the main contribution to the interaction at the interface (Figure 5, Supporting Information). The partial DOSs of the interfacial PO4 atoms in the aHA / rTiO2(Vo1) interface show new sharp peaks at −14.5 and −12.6 eV, and they overlap with the Ti states. Also the p orbital of Ca has an influence on the interaction at the interface, but the amplitude of the partial DOS of Ca is relatively lower that of the other atoms, implying a weak interaction between Ca and others atoms of the interface (Figure 5, Supporting Information). Also the charge density difference (CDD) may provide additional insight into the electronic interactions between aHA and different structures of rTiO2. The CDD are the calculated differences between the charge density of the interface systems and that of the isolated fragments. They illustrate how the charge density changes upon interaction. The CDD is defined as75: ∆ρ(r) = ρ(aHA/rTiO2(r)) − ρ(aHA(r)) − ρ(rTiO2(r)),


(2)


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where ρ(aHA/rTiO2(r)) is the charge density of the total aHA / rTiO2 interface system, and ρ(aHA(r)) and ρ(rTiO2(r)) are the charge densities for the isolated aHA and rTiO2 slabs, respectively. (a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 6. Charge density difference (CDD) between aHA and stoichiometric rTiO2 (a-b), defected rTiO2 (c-d and e-f, for Vo3 and Vo1, respectively) and aTiO2 (g-h) electron gain (yellow) and loss (light blue). The white, red, purple, blue, and orange spheres represent the H, O, P, Ca, and Ti atoms, respectively. The isosurface value is set to ±0.001 e/Å3 (a, c, e, g) 16 ACS Paragon Plus Environment

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and ±0.01 e/Å3 (b, d, f, h). Light blue shading (yellow) indicates negative (positive) isosurface value. Yellow regions show electron accumulation, and blue regions represent electron depletion. In this study, the precise CDD isosurfaces at the interfaces were studied for all models with the stacking position that gave us the highest value of the work of adhesion. The CDD isosurface plots (Figure 6) are generated using the VESTA 3 program.41 Figure 6 shows the CDD with isosurface values of ±0.01 eV/Å3 and ±0.001 eV/Å3, contributing to an understanding of the chemical bonding mechanism at the aHA / rTiO2 interfaces.76 The yellow and the blue areas represent the accumulation and depletion of electrons, respectively. As can be seen in Figure 6 (a, c, e and g) the electron charge rearrangements are mainly located in two near-boundary layers. Clearly, there is charge depletion near the O atoms from the rTiO2 slabs and charge accumulation near the Ca along the Ca–O direction. This indicates that there is charge transfer from O to Ca and a covalent bond between them is formed. There is the same character of the charge transfer between O atoms from the PO4 groups and Ti atoms along the Ti–O direction at the interfaces. Electronegative zones (yellow) are created by electron transfer from O atoms to Ti atoms, which lead to the electropositive zones at surface O atoms (blue). It can be seen that Ti atoms act as electrons acceptor (Lewis acid) for O atoms from the PO4 groups.77 Only little charge transfer is observed for the interaction between aHA and rTiO2(Vo3), indicating a weak interaction (Figure 6 (c, d)). The interfacial interactions are stronger for the interfaces between the aHA and crystalline rTiO2 (110) with the Vo1 vacancies and without any vacancies, than for the aHA / rTiO2 (110) interface with the Vo3 vacancies (Figure 6 (b, f)). The strongest interactions are observed in the case of the interface between the



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amorphous structures (Figure 6 (g, h)). This is also consistent with the fact that the work of adhesion of those interfaces is much higher than for the others. In summary, the aHA / aTiO2 interface shows a stronger interaction and is thermodynamically favoured over the aHA / c-rTiO2 interfaces. The dominant bonds are covalent interactions between interfacial atoms, especially Ti–O bonds between O atoms from the PO4 groups and Ti atoms from rTiO2 slabs. The bonding strength at the interface, measured by the work of adhesion, can be correlated with the integral charge transfer (ICT). Bader charge analysis was used to estimate the charge transfer in the simulations, as obtained from integrating the charge density over the grid points.78 We used the Bader code adapted by Sanville et al.,78 which outputs the total charge associated with each atom and the zero flux surfaces defining the Bader volumes. Thus, the ICT represents the exchange of electrons between one molecule to its nearest neighbor molecule, and is strongly affected by the intermolecular distance. The shorter the distance, the stronger the orbitals overlap resulting in a rise in the ICT.78 Table 3 represents the calculated ICT (electron transfer) at the interface for all systems. A negative value of ICT means that rTiO2 accepted electrons from aHA. The minimum values of ICT (i.e., with maximum absolute values) are −0.255, −0.161, −0.250, and −1.065 electron for the aHA / c-rTiO2, aHA / rTiO2 (Vo1), aHA / rTiO2 (Vo3), and aHA / aTiO2 interfaces, respectively. The obtained data shows that aHA becomes more positively charged after interaction for all models (Table 3), due to the donation of the electrons to the substrates. Note, however, that the total charge transfer is very small for all crystalline rTiO2 (110) surfaces, due to the rather weak interaction, in agreement with the calculated work of adhesion. In the case of the aTiO2 surface, the observed charge transfer is slightly larger, and the work of adhesion has a more negative value, indicating the stronger interfacial adhesion.


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It has been shown that the character of interactions at the aHA / rTiO2(Vo1) strongly depends on O vacancies and is slightly different from the others interface models. HA adsorption at a Vo1 site, leads to the formation of three Ti−O bonds in a range of 2.18-2.38 Å. Moreover, two covalent Ca-O bonds (2.29 and 2.45 Å) were detected. This analysis explains the little ICT at the aHA / rTiO2(Vo1) interface in comparison with other interface models between aHA and stoichiometric and reduced rTiO2, as it was above revealed that Ti4+ atoms as well as Ca2+ atoms behave as Lewis acid due to the reduced coordination at the interfaces. There are also two covalent Ca-O bonds (in a rage of 2.28-2.38 Å) and one strong Ti−O bond was detected (1.86 and 1.91 Å for aHA / c-rTiO2 and aHA / rTiO2(Vo3), respectively). The structural picture of the interaction at the aHA / aTiO2 shows three Ca−O bonds of about 2.43±0.07 Å and shorter Ti−O bond lengths (1.83 Å) compared to other models. Thus, aHA adsorption on rTiO2(Vo1) and aTiO2 surfaces was found to be more stable than on perfect rTiO2 and rTiO2(Vo3) surfaces. The presence of Vo1 defect in rTiO2 (110) leads to an increase in surface reactivity, in contrast to rTiO2 (Vo3). In addition, the chemistry of the rTiO2 surface can affect Ti−O and Ca-O bonds network character and thus influences the adhesion of aHA and the rearrangements of integral charge at the interface. Based on the observed ICT and a Lewis acid-base interpretation66, we found that the aHA adsorption on the rTiO2 surface is dictated by surface morphology and depend on the formed bond type and bond length.

Conclusion In conclusion, we carried out DFT calculations to determine the adhesion strength at the interface between the aHA and rTiO2 (110) surfaces in crystalline and amorphous states to obtain an atomistic insight of implant protection from failure. Six interface models with



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different stacking were considered. We carried out structural optimization and atomic relaxation of the bulk, surfaces, and interfaces. We found that after relaxation, the bottom crystalline Ti layers show a zigzag structure and strong distortion of atomic positions in the aHA side. Significant distortion of atoms during the optimization was observed in the cases of aTiO2 slabs as well. In particular, significant distortion of atomic positions occurred in the Ti side during the optimization. It was observed that the Ti−O and Ca−O bonds is preferentially formed across the interface for all models. The analysis of obtained electronic structure reveals that the p orbital of Ca, d orbital of Ti and p orbital of PO4 in the valence band made the main contributions to the interaction at the interface. The investigation of the adhesive energy between the rTiO2 (110) and aHA slabs shows that vacancies have only a very weak influence on the bonding strength at the interface. Finally, comparison of results obtained for crystalline rTiO2 (110) with or without vacancies and aTiO2 reveals the strong interaction only for the latter.

Acknowledgements The authors are thankful to Samira Dabaghmanesh and Maksudbek Yusupov from the University of Antwerp (Belgium) for useful discussions, and to Dr. Konstantin Ivanov and Mark Kalashnikov from the Institute of Strength Physics and Materials Science, Siberian Branch of Russian Academy of Sciences for their generous assistance with TEM investigations. This work was financially supported by the “P.L.U.S.” scholarship funded by National Research Tomsk Polytechnic University, BOF Fellowships for International Joint PhD students funded by University of Antwerp (project number 32545), S.H. is funded as PhD fellow (aspirant) of the FWO-Flanders (Fund for Scientific Research-Flanders), Grant number 11C0115N. Federal Target Program #14.587.21.0013 (application 2015-14-588-


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0002-5599),

President's

fellowships

МК-7907.2016.8,

МК-6459.2016.8,

and

11.1233.2017/4.6.

Associated Content Supporting Information The rTiO2 (110) surface energy as a function of the slab thickness, side view of the rTiO2 (110) slab model, oxygen vacancy formation energies and partial DOS for optimized aHA / rTiO2(Vo1) interface, Figure S1, Figure S2, Table S1 and Figure S3, respectively. Final CONTCAR files for all considered models in the case of best stacking position. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Density Functional Theory Study of Interface Interactions in

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