Experimental Visualization of Chemical Bonding and Structural

ARTICLE pubs.acs.org/JPCC

Experimental Visualization of Chemical Bonding and Structural Disorder in Hydroxyapatite through Charge and Nuclear-Density Analysis Masatomo Yashima,*,†,‡ Yukihiko Yonehara,‡ and Hirotaka Fujimori§ †

Department of Chemistry and Materials Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1-W4-17, O-okayama, Meguro-ku, Tokyo, 152-8551, Japan ‡ Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan § Department of Applied Chemistry, Faculty of Engineering, Yamaguchi University, 2-16-1 Tokiwadai, Ube, Yamaguchi 755-8611, Japan

bS Supporting Information ABSTRACT: Calcium hydroxyapatite (HAp, Ca10(PO4)6(OH)2) is the principal inorganic component of bone and teeth, bioactive material, and proton (H+) conductor. However, the chemical bonding and structural disorder of HAp are unclear. Here we report precise chargeand nuclear-density distributions of HAp at 298 and 673 K. The present results clearly demonstrate the covalent PO and OH bonds, more ionic CaO bonds, and the charge transfers from P to O atoms and from H to O atoms in HAp. This work shows that the hexagonalmonoclinic phase transition of HAp is accompanied by the occupational and orientational ordering of OH ions, the tilting of the PO4 tetrahedron, and the Ca displacements. Diffusion paths of proton are visualized along the c-axis in hexagonal HAp. We anticipate that the visualization of chemical bonding and structural disorder of HAp will contribute greatly to our understanding of biominerals, reactions, biological organisms, and the diffusion process in HAp-based proton conductors.

1. INTRODUCTION Calcium hydroxyapatite is the biomineral most relevant for our day-to-day lives because it forms the main constituent of bone and teeth.1 Calcium hydroxyapatite has successfully been applied in medicine due to its excellent biocompatibility,2 and it can be used as intermediate-temperature fuel cells and chemical sensors.3 The crystal structure of calcium hydroxyapatite consists of the PO4 tetrahedron, OH and Ca2+ ions.46 The stoichiometric (Ca/P atomic ratio = 5:3) Ca10(PO4)6(OH)2 (HAp) is the mother material of calcium hydroxyapatites. HAp exhibits a phase transition between the low-temperature monoclinic (space group P21/c) and high-temperature hexagonal (P63/m) phases at around 483 K.615 There have been many debates on the mechanism of the monoclinichexagonal phase transition in HAp,415 but the mechanism is unclear. Most of the biomineral hydroxyapatites are the hexagonal phase, which might be a disordered state of ordered monoclinic phase. Thus, the crystallographic study of the monoclinichexagonal phase transition in HAp is the key to understanding the bones and teeth at an atomic scale. Detailed experimental studies of the structural change between the monoclinic and hexagonal HAp are required. The charge density distribution of a solid is of vital importance in many fields of chemistry, physics, and materials science.1618 The charge density distribution of a solid provides the information not only on the details of crystal structure but also on the r 2011 American Chemical Society

chemical bonding. Charge density distribution of HAp obtained by the density functional theory (DFT) calculations at 0 K suggested the covalent PO and OH bonds.1922 Providing experimental evidence for the covalent bonds in HAp is an important challenge in the science and engineering of calciumphosphate-based materials. Young et al.23 and Suetsugu et al.24 reported the Fourier maps of HAp. Okazaki et al.25 reported the charge density distribution of HAp. However, the chemical bonding in HAp has not been clarified yet through experimental electron-density distributions. The HAp, Ca10(PO4)6(OH)2, contains a hydroxyl anion OH. In the hydroxyl anion, the hydrogen might be bound covalently to the oxygen atom. However, there exists no experimental evidence of the covalent OH bonds in the previous charge density studies of HAp. In the present work, we examine the charge-density distributions of HAp through synchrotron diffraction experiments, to investigate its chemical bonding. HAp is a proton (H+) conductor.3,26 The proton diffusion in HAp is important to understand the chemical and biological reactions in the tooth and bones and acid attack on the tooth, which leads to caries lesions.26 Proton transport along the c axis of HAp is suggested to be responsible for its polarization, which Received: September 9, 2011 Revised: October 29, 2011 Published: October 31, 2011 25077

dx.doi.org/10.1021/jp208746y | J. Phys. Chem. C 2011, 115, 25077–25087

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Figure 1. FT-IR spectrum of Ca10(PO4)6(OH)2. PO43 bands appear around 600 and 1100 cm1. The OH band exists at 3570 cm1. There are no bands of CO32 around 1500 and 700 cm1.

Figure 2. Rietveld patterns of synchrotron and neutron powder diffraction data of Ca10(PO4)6(OH)2 (HAp) at 298 and 673 K. Synchrotron data at 298 K (a, b) and at 673 K (c, d). Neutron data at 298 K (e) and at 673 K (f). Red plots denote observed data; green line denotes calculated profiles; and blue line denotes the difference. Vertical lines indicate possible Bragg peaks of (a, b, e) the monoclinic and (c, d, f) hexagonal phases. Arrows in (b) stand for the monoclinic reflections forbidden for the hexagonal HAp. Wavelengths of incident synchrotron X-ray and neutron are 1.197146(2) and 1.8449(1) Å, respectively.

leads to remarkable biological responses and enhanced bone formation.27 Geometric information of the proton diffusion in a unit cell of HAp is essential for the mechanism of proton conduction. The proton diffusion path has been examined by molecular dynamics calculations.16 However, the diffusion path of the proton in HAp has not been investigated experimentally. In the present work, the nuclear-density distributions of HAp were studied through the neutron diffraction experiments, to investigate the proton diffusional pathway.

2. MATERIALS AND METHODS 2.1. Sample Preparation and Characterization. A stoichiometric (Ca/P = 5:3) hydroxyapatite sample without impurity phases was prepared by a gel route.28 Calcium nitrate (Ca(NO3)2, phosphonoacetic acid (HOOCCH2PO(OH)2), and anhydrous citric acid (C6H8O7) were used as starting materials. An aqueous clear solution was obtained by dissolving Ca(NO3)2 powder into distilled water at room temperature. The anhydrous citric acid 25078

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was dissolved into this solution in a beaker, on a stirrer with a heater. The mixing molar ratio was Ca(NO3)2:C6H8O7 = 1:2. After the solution became transparent, a phosphonoacetic Table 1. Refined Crystallographic Parameters and Reliability Factors in the Rietveld Analysis of Synchrotron X-ray Powder Diffraction Data of Ca10(PO4)6(OH)2 at 298 Ka atom site occupancy

x

y

z

U (Å2)

Ca1

4e

1.0

0.8301(3)

0.50059(1)

Ca2

4e

1.0

0.8317(3)

0.99717(13) 0.58783(11) 0.0089(5)

0.58120(12) 0.0104(5)

Ca3 Ca4

4e 4e

1.0 1.0

0.2460(2) 0.2545(2)

0.7543(2) 0.2449(2)

0.2460(1) 0.6241(1)

Ca5

4e

1.0

0.4935(2)

0.2556(2)

0.37445(11) 0.0098(5)

P1

4e

1.0

0.8966(3)

0.7533(2)

0.26400(13) 0.0066(6)

P2

4e

1.0

0.8688(3)

0.2530(3)

0.44921(14) 0.0076(6)

P3

4e

1.0

0.4683(3)

0.7542(3)

0.43385(14) 0.0072(6)

O1

4e

1.0

0.1731(8)

0.2628(6)

0.3268(4)

0.0094(5)

O2

4e

1.0

0.0112(7)

0.7491(7)

0.5831(3)

= U(O1)

O3 O4

4e 4e

1.0 1.0

0.6588(7) 0.0877(8)

0.7549(7) 0.7396(6)

0.4913(4) 0.3111(4)

= U(O1) 0.0108(5)

0.0087(5) 0.0082(5)

O5

4e

1.0

0.9649(8)

0.2329(6)

0.5434(4)

= U(O4)

O6

4e

1.0

0.3780(8)

0.7350(6)

0.4818(4)

= U(O4)

O7

4e

1.0

0.8462(6)

0.5721(8)

0.2952(3)

0.0091(5)

O8

4e

1.0

0.7456(6)

0.0867(9)

0.4099(3)

= U(O7)

O9

4e

1.0

0.4279(6)

0.5835(8)

0.3747(3)

= U(O7)

O10 4e

1.0

0.8639(6)

0.9426(8)

0.2983(3)

= U(O1)

O11 4e O12 4e

1.0 1.0

0.7682(6) 0.4134(7)

0.4419(9) 0.9320(9)

0.4299(4) 0.3798(3)

= U(O1) = U(O1)

O13 4e

1.0

0.4987(10) 0.8020(2)

0.2475(5)

0.0127(6)

H

1.0b

0.529c

0.257c

0.034c

4e

0.950c

a

Space group: P21/c. Unit-cell parameters: a = 9.42024(7) Å, b = 6.88249(1) Å, c = 18.84590(15) Å, α = γ = 90°, β = 120.0000(7)°. Atomic coordinates: x, y, z. Atomic displacement parameters: U. Reliability factors: Rwp = 5.10%, RI = 2.91%, RF = 1.34%. Goodness of fit: Rwp/Re = 1.68. Reliability factors after 1st MPF: Rwp = 4.98%. Goodness of fit: Rwp/Re = 1.64; RI = 1.41%, RF = 0.81%. b The occupancy factor of the H atom was refined to be unity within the estimated standard deviation in the Rietveld analysis of neutron data at the same temperature. Thus, it was fixed to be unity in this refinement. c Positional and thermal parameters of the H atom were fixed to the values obtained by the Rietveld analysis of neutron data.

acid aqueous solution was mixed with this solution in the stoichiometric atomic ratio of Ca/P = 5:3. The colorless clear solution thus obtained was heated with stirring where the setting temperature of the stirrer was 473 K. As the solution became concentrated, its color changed from colorless to yellow, and then the solution became highly viscous, accompanied with evolution of gas. The gel thus obtained was converted to a brown powder after removing the excess of solvent. The brown powder was heated at 1073 K under flowing oxygen gas for 2 h. The material thus obtained was heated at 1273 K under flowing pure Ar gas saturated with water vapor for 24 h. The purity and compositional homogeneity of the HAp sample were examined by Inductively Coupled Plasma (ICP) spectroscopy, Infra-Red (IR, Perkin-Elmer Spectrum 2000) spectroscopy (Figure 1), thermal stability in air at 1273 K, and Rietveld analyses of neutron and synchrotron powder diffractometry. The refined unit-cell parameters of the present HAp agree with those in the literature.14 2.2. Neutron Diffraction. We collected neutron powder diffraction data in air at 298 and 673 K with a homemade furnace29 and an angle dispersive type neutron powder diffractometer HERMES,30 of the Institute for Materials Research (IMR), Tohoku University, installed in the JRR-3M reactor at the Japan Atomic Energy Agency (JAEA), Tokai, Japan. Neutrons with wavelengths of 1.84491 and 1.84780 Å were obtained by 331 reflections of the Ge monochromator and 120 -blanksample-220 collimation for the measurements at 298 and 673 K, respectively. The HAp material was mounted in the hightemperature furnace, which was set on the sample table of the HERMES diffractometer.30 The diffracted beam was detected by a 150 3He detector system with Cd blades and slits in the 2θ range of 5155° at intervals of 0.1°. The collected data were analyzed by the Rietveld method and MEM-based pattern fitting with the computer program RIETAN-FP31 and PRIMA.32 Peak profile shape was approximated by split pseudo-Voigt function, and the background profile was approximated with a 12-parameter Legendre polynomial. The unit cell, zero point, background, profile shape, and crystal structural parameters were simultaneously refined. The coherent scattering length adopted for Rietveld refinements were 4.70 fm for Ca, 5.13 fm for P, 3.739 fm for H, and 5.803 fm for O. The nuclear-density distributions of monoclinic and hexagonal HAp were investigated by the maximum-entropy method (MEM) using the 1053 and 202 structure factors, respectively, obtained by the Rietveld

Table 2. Refined Crystallographic Parameters and Reliability Factors in the Rietveld Analysis of Synchrotron X-ray Powder Diffraction Data of Ca10(PO4)6(OH)2 at 673 Ka y

z

U (Å2)

1/3

2/3

0.00183(9)

0.02520(11)

0.24706(5)

0.99291(6)

1/4

0.02386(9)

0.39878(6)

0.36936(5)

1/4

0.00806(10)

1.0

0.32931(14)

0.48429(14)

1/4

0.0217(4)

6h

1.0

0.58544(15)

0.46359(16)

1/4

0.0274(5)

O3

12i

1.0

0.34368(12)

0.26021(12)

0.07205(14)

0.0289(3)

O4

4e

0.5

0

0

0.2025(4)

0.0291(8)

H

4e

0.5b

0

0

0.062c

atom

site

occupancy

Ca1

4f

1.0

Ca2

6h

1.0

P1

6h

1.0

O1

6h

O2

x

0.082c

Space group: P63/m. Unit-cell parameters: a = b = 9.47907(2) Å, c = 6.91842(1) Å, α = β = 90°, γ = 120°. Atomic coordinates: x, y, z. Atomic displacement parameters: U. Reliability factors: Rwp = 6.06%, RI = 5.45%, RF = 4.79%. Goodness of fit: Rwp/Re = 1.79. Reliability factors after 1st MPF: Rwp = 5.96%, RI = 3.27%, RF = 2.83%. Goodness of fit: Rwp/Re = 1.75. b The occupancy factor of the H atom was refined to be 0.5 within the estimated standard deviation in the Rietveld analysis of neutron data at the same temperature. Thus, it was fixed to be 0.5 in this refinement. c Positional and thermal parameters of the H atom were fixed to the values obtained by the Rietveld analysis of neutron data. a

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Table 3. Refined Crystallographic Parameters and Reliability Factors in the Rietveld Analysis of Neutron Powder Diffraction Data of Ca10(PO4)6(OH)2 at 298 Ka atom site occupancy

x

y

z

Table 4. Refined Crystallographic Parameters and Reliability Factors in the Rietveld Analysis of Neutron Powder Diffraction Data of Ca10(PO4)6(OH)2 at 673 Ka

U (Å2)

atom site occupancy

x

y

z

U (Å2)

1/3

2/3

Ca1

4e

1.0

0.837(4) 0.508(2)

0.582(2)

0.005(2)

Ca1

4f

1.0

0.0031(7)

0.0199(15)

Ca2

4e

1.0

0.827(4) 0.995(2)

0.585(2)

= U(Ca2)

Ca2

6h

1.0

0.2442(6) 0.9936(6)

1/4

0.0100(10)

Ca3

4e

1.0

0.243(3) 0.755(4)

0.2468(15) 0.0076(16)

P1

6h

1.0

0.3977(5) 0.3685(4)

1/4

0.0144(9)

Ca4

4e

1.0

0.264(3) 0.257(5)

0.6261(17) = U(Ca3)

O1

6h

1.0

0.3306(4) 0.4859(4)

1/4

0.0213(9)

Ca5 P1

4e 4e

1.0 1.0

0.493(3) 0.237(5) 0.888(3) 0.751(3)

0.3707(18) = U(Ca3) 0.2611(13) 0.0075(15)

O2 O3

6h 12i

1.0 1.0

0.5870(4) 0.4662(5) 0.3441(3) 0.2605(3)

1/4 0.0729(3)

0.0262(10) 0.0272(6)

P2

4e

1.0

0.868(3) 0.251(4)

0.4482(16) = U(P1)

O4

4e

0.5

0

0

P3

4e

1.0

0.461(3) 0.735(4)

0.4341(14) = U(P1)

H

4e

0.5

0

0

O1

4e

1.0

0.172(3) 0.256(4)

0.3252(15) 0.0104(14)

O2

4e

1.0

0.014(3) 0.759(4)

0.5875(14) = U(O1)

O3

4e

1.0

0.655(3) 0.751(4)

0.4943(16) = U(O1)

O4

4e

1.0

0.085(3) 0.750(4)

0.3069(15) 0.0115(15)

O5 O6

4e 4e

1.0 1.0

0.958(3) 0.248(4) 0.378(3) 0.734(4)

0.5425(14) = U(O4) 0.4849(14) = U(O4)

O7

4e

1.0

0.833(3) 0.579(4)

0.2889(17) 0.013(2)

O8

4e

1.0

0.747(3) 0.076(4)

0.4165(16) = U(O7)

O9

4e

1.0

0.421(3) 0.584(4)

0.3768(17) = U(O7)

O10

4e

1.0

0.842(3) 0.940(4)

0.2928(15) 0.007(2)

O11

4e

1.0

0.772(3) 0.450(3)

0.4329(13) = U(O10)

O12

4e

1.0

0.411(3) 0.919(3)

0.3837(14) = U(O10)

O13 H

4e 4e

1.0 1.0

0.499(4) 0.8012(13) 0.249(2) 0.529(5) 0.950(3) 0.257(4)

0.013(3) 0.034(10)

a Space group: P21/c. Unit-cell parameters: a = 9.4194(8) Å, b = 6.8814(2) Å, c = 18.8495(15) Å, α = γ = 90°, β = 119.993(5)°. Reliability factors in the Rietveld analysis: Rwp = 4.57%, RI = 0.91%, RF = 0.38%. Goodness of fit: Rwp/Re = 3.84.

analyses. MEM calculations of monoclinic and hexagonal HAp were carried out using a computer program PRIMA32 with 48 34 94 and 94 94 70 pixel unit cells, respectively. The crystal structure and density distributions were visualized using the VESTA computer program.33 2.3. Synchrotron Diffraction. Synchrotron X-ray powder diffraction analyses were performed using the multiple-detector system34 and an electric furnace35,36 installed at the BL-4B2 beamline of the Photon Factory operated by the High Energy Accelerator Research Organization (KEK), Japan. The experimental setup consisted of a bending-magnet light source, a double-crystal Si(111) monochromator, a focusing cylindrical mirror, and a multiple-detector system with Ge(111) analyzer crystals, Soller slits, and scintillation counters. A monochromatized 1.197146(2) Å X-ray beam was utilized. Powder diffraction data from the powdered HAp sample at 298 and 673 K in air were collected in asymmetric flat-specimen reflection geometry with a fixed incident angle of 7.0°. Scanning parameters were set as follows: step interval, 0.004°; counting time, 4 s step1; diffraction angle (2θ), 8150°. The crystal structure of HAp was refined by the Rietveld method using RIETAN-FP.31 As enhancement in asymmetric scan mode is not implemented in RIETAN-FP, the observed intensity data were modified by multiplying by the term [1 + {sin α/sin(2θ α}]/2, where α is the fixed incident angle, to obtain data equivalent with those measured in symmetric scan mode. The peak shape was assumed to be a split Pearson VII-type function, and the cutoff value was set at 30 times the full-width at half-maximum

0.1983(12) 0.021(2) 0.062(3)

0.082(9)

a

Space group: P63/m. Unit-cell parameters: a = b = 9.4794(3) Å, c = 6.91507(14) Å, α = β = 90°, γ = 120°. Reliability factors: Rwp = 4.26%, RI = 1.24%, RF = 0.57%. Goodness of fit: Rwp/Re = 3.79.

(fwhm). The background was approximated with a 12-parameter Legendre polynomial. The 12 variables were refined simultaneously with the unit-cell, zero point, scale, profile shape, and crystal structural parameters. The electron-density distributions of monoclinic and hexagonal HAp were investigated by the maximum-entropy method (MEM) using the 4525 and 825 structure factors, respectively, obtained by the Rietveld analyses. MEM calculations of monoclinic and hexagonal HAp were carried out using a computer program PRIMA32 with 46 34 94 and 94 94 70 pixel unit cells, respectively. To confirm the validity of the MEM analysis, MEM-based pattern fitting (MPF)32 was also conducted using the structure factors obtained by Fourier transform of the MEM electron density distribution. 2.4. Density Functional Theory Based Calculations. The generalized gradient approximation (GGA) electronic calculations were performed with the Vienna Ab initio Simulation Package (VASP),37 to examine the electron-density distributions and optimized crystal structures of HAp. A plane-wave basis set with a cutoff of 500 eV was used. The PerdewBurkeErnzerhof (PBE) GGA was employed for the exchange and correlation functionals. Atomic coordinates were optimized with the convergence condition of 0.01 eV/Å. The positions of all atoms were relaxed. Unit-cell and initial positional parameters used in the optimization were referred from the Rietveld refinements in this study. Crystal structures and valence electron density distributions were drawn with a computer program VESTA.33 The density of states and band structure of monoclinic HAp are shown in Figures S1 and S2 in the Supporting Information.

3. RESULTS AND DISCUSSION 3.1. Characterization of the Hydroxyapatite Sample. A HAp sample without impurity phases was obtained by a gel route.28 The chemical composition of the present sample was confirmed to be stoichiometric Ca10(PO4)6(OH)2 by Inductively Coupled Plasma (ICP) spectroscopy, Infra-Red (IR) spectroscopy (Figure 1), thermal stability in air at 1273 K, and Rietveld analyses of neutron and synchrotron powder diffraction data. The present HAp is single monoclinic phase at 298 K as evidenced by some peaks observed in the synchrotron diffraction data at this temperature (arrows in Figure 2b). These monoclinic reflections disappear at 673 K (Figure 2d), which indicates the hexagonal phase at this temperature. The monoclinic-to-hexagonal phase transformation in the present HAp between 298 and 25080



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Table 5. Selected Bond Lengths, Coordination Number (CN), Bond Valence Sum (BVS), Volume of Polyhedron, Quadratic Elongation, and Bond Angle Variance in Monoclinic Hydroxyapatite.

Table 5. Continued PO4 group details CN = 4 BVS = 4.821

O2 O11

Ca environments

O5

Ca1

O6

2.376(5) Å

CN = 7

O1

2.392(6) Å

BVS = 1.927

O3

2.400(6) Å

O2

2.418(8) Å

O4

2.437(8) Å

O5

2.523(6) Å

O11 volume of (Ca1)O7 polyhedron

2.391(6) Å

CN = 8

O1

2.406(5) Å

O5

2.431(6) Å

O2

2.443(8) Å

O4

2.447(7) Å

O6

2.521(5) Å

O12

2.676(8) Å

O10

2.690(4) Å

volume of (Ca2)O8 polyhedron O10

2.342(8) Å

CN = 7

O7

2.344(8) Å

BVS = 1.977

O4

2.371(6) Å

O13

2.389(12) Å

O9

2.485(8) Å

O12

2.536(8) Å

O2

2.703(8) Å

volume of (Ca3)O7 polyhedron

1.0021

bond angle variance

8.4737 deg2

O12

1.518(9) Å

O6

1.535(6) Å

BVS = 4.808

O9 O3

1.545(8) Å 1.546(5) Å

volume of (P3)O4 polyhedron

1.856 Å3

quadratic elongation

1.0014

bond angle variance

5.0848 deg2

Table 6. Selected Bond Lengths, Coordination Number (CN), Bond Valence Sum (BVS), Volume of Polyhedron, Quadratic Elongation, and Bond Angle Variance in Hexagonal Hydroxyapatite at 673 K Ca environments

26.32 Å3

Ca3


CN = 4

2.624(6) Å

O3

1.550(10) Å 1.851 Å3

P3

20.72 Å3

Ca2 BVS = 1.971


1.531(7) Å 1.533(7) Å

Ca1 CN = 9

O1, O10 , O100 O2, O20 , O200

BVS = 1.937

O3, O30 , O300 volume of (Ca1)O9 polyhedron

2.4232(7) Å 2.4705(7) Å 2.8272(6) Å 32.68 Å3

Ca2

O1

2.7249(13) Å

CN = 8

O2

2.3800(10) Å

BVS = 2.185

O3, O30

2.3652(9) Å

O300 , O3000

2.5404(12) Å

21.91 Å3

O4, O40 volume of (Ca2)O8 polyhedron

2.3988(7) Å 23.95 Å3

Ca4

O11

2.356(7) Å

CN = 7

O5

2.359(5) Å

BVS = 1.945

O8

2.363(7) Å

O13

2.400(7) Å

P1

O1

O7

2.467(6) Å

CN = 4

O2

1.5323(10) Å

O10

2.554(5) Å

BVS = 4.930

O3, O30

1.5227(9) Å

O3 volume of (Ca4)O7 polyhedron

2.717(5) Å

O9

2.329(8) Å

CN = 7 BVS = 2.046

O6 O13

2.345(9) Å 2.353(6) Å

O12

2.367(8) Å

O8

2.426(7) Å

O11

2.582(6) Å

O1

2.695(8) Å 21.70 Å3

PO4 group details P1 CN = 4 BVS = 4.765

O1 O10

P2

1.520(10) Å 1.542(7) Å

O7

1.546(7) Å

O4

1.550(6) Å


1.867 Å3


1.0018

bond angle variance

7.8724 deg2

O8


22.08 Å3

Ca5

volume of (Ca5)O7 polyhedron

PO4 group details

1.527(6) Å

1.5290(14) Å

1.823 Å3


1.0011

bond angle variance

4.1183 deg2

673 K is consistent with the transition temperature at around 483 K reported in the previous works.9,14,15 3.2. Synchrotron and Neutron Diffraction Measurements of Hydroxyapatite. Synchrotron X-ray diffraction data include useful information on the chemical bonding. To obtain accurate electron density distribution of HAp, we collected the data by reflection geometry with a high-angular-resolution synchrotron powder diffractometer34,38 (angular resolution, Δd/d = 0.04%, d and Δd are lattice spacing and full width at half-maximum in the d scale, respectively). Neutron diffraction profiles give useful information on hydrogen and oxygen because the scattering ability of the hydrogen and oxygen nuclei (amplitude of coherent scattering length) is relatively large and independent of diffraction angle. This nature enables detailed analysis of the small amount of hydrogen atoms, nuclear density distribution, structural disorders, thermal motion, and diffusional pathway of hydrogen and oxygen atoms in HAp. Furthermore, the 25081



Figure 3. Refined crystal structures of (a) monoclinic and (b) hexagonal HAp at 296 and 673 K, respectively, through Rietveld analysis of synchrotron powder diffraction data. Both monoclinic and hexagonal structures of HAp consist of PO4 tetrahedra, OH and Ca ions and are similar to each other.

neutron diffraction is a powerful method to collect quality data at high temperatures.18,29 In the present work, we did not use the deuterium (D) substituted calcium hydroxyapatite (Ca10(PO4 )6(OD)2) but used the nonsubstituted HAp (Ca10(PO4 )6(OH)2), to distinguish the hydrogen with minus scattering length from hydrogen-bonded oxygen with plus scattering length. 3.3. Rietveld Analysis and Crystal Structure of Hydroxyapatite. Rietveld analyses of synchrotron and neutron diffraction data of HAp measured at 298 and 673 K were successfully performed by the monoclinic P21/c and hexagonal P63/m structures, respectively (Figure 2). In preliminary analyses of neutron data at 298 and 673 K, the refined occupancy factors of the H atom in the monoclinic and hexagonal HAp were refined to be 1.00(4) and 0.496(15), respectively. Thus, the occupancy factors of the H atom in the monoclinic and hexagonal phases were fixed to be 1.00 and 0.50, respectively, in the subsequent analyses. The refined crystallographic parameters from synchrotron and neutron data are listed in Tables 14. The reliability factors for the analysis of neutron data of HAp at 298 K were Rwp = 4.57%, RI = 0.91%, and RF = 0.38%, and those at 673 K were Rwp = 4.26%, RI = 1.24%, and RF = 0.57% (Tables 3 and 4). The reliability factors for the analysis of synchrotron data of HAp at 298 K were Rwp = 5.10%, RI = 2.91%, and RF = 1.34%, and those at 673 K were Rwp = 6.06%, RI = 5.45%, and RF = 4.79% (Tables 1 and 2). The refined atomic position and atomic displacement parameters of the H atom obtained in the Rietveld analysis of neutron data were used and fixed in the analyses of synchrotron X-ray data because these parameters were difficult to be determined only from the synchrotron data due to the charge transfer from the H to O atom as described below. The unit-cell and structural parameters of HAp from synchrotron data agreed well with those from neutron data. The refined crystallographic parameters of the present monoclinic HAp also agreed with those obtained by the single-crystal neutron and X-ray diffraction analyses reported in the literature.6,24 The refined crystallographic parameters of hexagonal P63/m HAp at 673 K are in good agreement with those after S€anger and Kuhs,40 although they analyzed the room-temperature data

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by invalid space group P63/m. The bond valence sum (BVS) of Ca sites ranges from 1.9 to 2.2, which is consistent with the valence +2 of Ca2+ (Tables 5 and 6). The BVS of P is estimated to be 4.84.9, which agrees with the valence +5 of P5+ (Tables 5 and 6). Positional parameters of the optimized structures through Density Functional Theory (DFT) calculations agree with those from neutron and synchrotron data (Tables S1 and S2 in the Supporting Information). These results indicate the validity of the present crystal structure analysis of HAp. Both monoclinic and hexagonal structures of HAp consist of PO 4 tetrahedra, OH and Ca 2+ ions and are similar to each other (Figures 3, 4a, and 4b). The monoclinic HAp exhibits the OH orientational ordering (O13H in Figure 4a), which makes the doubled c-axis length compared with the corresponding b-axis length of hexagonal HAp (Figure 4b). The distortions of PO 4 in both monoclinic and hexagonal HAps are small (Tables 5 and 6). The distortions of PO 4 in monoclinic HAp are a little larger than that in hexagonal HAp. 3.4. Electron-Density Analysis of Hydroxyapatite. To evaluate the chemical bonding, charge transfer, and structural disorder in HAp, the maximum-entropy method (MEM) and MEM-based pattern fitting (MPF)18,32 were applied to estimate the electron- and neutron-scattering-length- (nuclear-) density distributions. MEM is a model-free method used to calculate precise electron and nuclear densities in solids, including the information on the disorder, anharmonic vibrations, and/or covalent bonds using experimentally obtained structure factors as an initial input. Successful MEM and MPF enhancements make it possible to evaluate not only the missing and heavily overlapped reflections but also any type of complicated electronor nuclear-density distribution, which is hard to describe with a classical structure model. In MEM, any type of complicated electron- or nuclear-density distribution, is allowed as long as it satisfies the symmetry requirements. The validity of such a methodology has been well established for various materials.18,39 The reliability factors in MPF of the present synchrotron data at 673 K (RI = 3.27%, RF = 2.83%) were much lower than those in Rietveld analyses (RI = 5.45%, RF = 4.79%), which is attributable to the structural disorder and chemical bonding in the hexagonal HAp. An important question is whether the MEM electron density provides experimental evidence for the chemical bonding in HAp. Figures 4e and 4f clearly indicate the PO and OH covalent bonding within PO4 and OH groups, respectively. These figures also show ionic bonds between Ca and O atoms of the phosphate and hydroxyl groups. The minimum charge density at the PO bonds in monoclinic HAp at 293 K (average value = 1.40(10) Å3) is higher than that at the CaO bonds (average value = 0.22(6) Å3) (Table 7), which corresponds to the shorter PO bond length (average value = 1.54(2) Å) compared with CaO distance (average value = 2.46(12) Å). Minimum charge density at the PO bonds in hexagonal HAp at 673 K (average value = 1.6(2) Å3) is also higher than that at the CaO bonds (average value = 0.26(6) Å3) (Table 8), which corresponds to the shorter PO bond length (1.528(5) Å) compared with CaO distance (2.52(17) Å). These experimental values in the monoclinic and hexagonal HAp agree well with those from the DFT calculations (Tables 7 and 8), which indicates the validity of the present experimental electron-density distributions of monoclinic and hexagonal HAp. The valence charge density distribution clearly indicates the charge transfer 25082



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Figure 4. Chemical bonding, electron and nuclear densities and structures of monoclinic and hexagonal hydroxyapatite (HAp). a,b. Crystal structures projected on the bc planes of (a) monoclinic P21/c HAp at x = 0.5 and (b) P63/m hexagonal HAp at x = 0.0, which were obtained by the Rietveld refinements of synchrotron powder diffraction data taken in situ at (a) 298 and (b) 673 K, respectively. Experimental (c,d) nuclear- and (e,f) electrondensity distributions of (c,e) P21/c and (d,f) P63/m HAps obtained by the combined technique of maximum-entropy-method (MEM), MEM-based pattern fitting and Rietveld analysis of (c,d) the neutron and (e,f) synchrotron data ((c,e) 298 K and (d,f) 673 K). (g,h) Theoretical electron density distributions on the bc planes of (g) P21/c and (h) P63/m HAps obtained by the first-principle density functional theory (DFT) calculations. PO and OH bonds are shown in (a) and (b). Electron density maps (eh) clearly indicate both PO and OH covalent bonds.

from P to oxygen atom in monoclinic and hexagonal HAp (see Figure S3 in the Supporting Information). A striking feature of the electron-density distribution maps in Figures 4 and 5 is the charge transfer from a hydrogen to oxygen atom. Around the hydrogen atom, the electron density is extremely low. Thus, the hydrogen atom in HAp is regarded as a proton. The electron density around the oxygen atom bonded to the hydrogen is anisotropic due to the OH covalent bonding and the charge transfer from the H to O atom (Figures 5b and 5e), which is consistent with the results of DFT calculations (Figures 5c and 5f). The experimental electron density around the O(H) atom is more isotropic compared to the theoretical one, which is attributable to large thermal motions of the hydrogen atom. Here O(H) is the oxygen atom bound to the H atom.

3.5. Crystal Structure Change and Phase Transition Mechanism of Hydroxyapatite. Crystal structure and

nuclear-density distribution of monoclinic and hexagonal HAp in Figures 4a, 4b, 4c, 4d, 5a, and 5d indicate the mechanism of the monoclinichexagonal phase transition. In the hexagonal HAp, there are two mirror planes at z = 1/4 and 3/4 in Figures 4b, 4d, and 4f, while the monoclinic structure does not have the mirror planes. On a hexagonal axis, the direction of OfH is either up or down in the monoclinic HAp, while in the hexagonal HAp there exist both up and down hydroxyl OH ions where the probabilities of up and down OH ions are 50%. This result is the experimental evidence of orientational order disorder nature of the monoclinichexagonal phase transition. There are two oxygen and hydrogen sites for OH ions. In monoclinic HAp, one oxygen and one hydrogen sites are fully 25083



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Table 7. Minimum Electron Density Obtained by the Combined Technique of Maximum-Entropy Method (MEM) and Minimum Valence-Electron Density Obtained by the First-Principle Density Functional Theory (DFT) Calculations of Monoclinic Hydroxyapatite at 298 K bond

minimum electron density [Å3]

minimum valence-electron density [Å3]

bond length [Å]

bond length [Å]

Ca1O1

0.21

2.390(5)

0.22

2.39428

Ca1O2 Ca1O3 Ca1O4 Ca1O5 Ca1O6 Ca1O11 Ca2O1 Ca2O2 Ca2O3 Ca2O4 Ca2O5 Ca2O6 Ca2O10 Ca2O12 Ca3O2 Ca3O4 Ca3O7 Ca3O9 Ca3O10 Ca3O12 Ca3O13 Ca4O3 Ca4O5 Ca4O7 Ca4O8 Ca4O10 Ca4O11 Ca4O13 Ca5O1 Ca5O6 Ca5O8 Ca5O9 Ca5O11 Ca5O12 Ca5O13 average CaO P1O1 P1O4 P1O7 P1O10 P2O2 P2O5 P2O8 P2O11 P3O3 P3O6 P3O9 P3O12 average PO

0.20 0.25 0.18 0.20 0.25 0.28 0.33 0.29 0.24 0.30 0.19 0.20 0.17 0.26 0.14 0.30 0.35 0.13 0.17 0.16 0.18 0.15 0.26 0.15 0.27 0.11 0.18 0.18 0.16 0.27 0.20 0.25 0.10 0.26 0.25 0.22(6) 1.40 1.35 1.31 1.47 1.44 1.41 1.35 1.37 1.26 1.63 1.35 1.50 1.40(10)

2.403(6) 2.409(5) 2.425(6) 2.534(5) 2.357(4) 2.641(6) 2.422(4) 2.436(6) 2.404(5) 2.458(6) 2.441(5) 2.536(4) 2.617(3) 2.711(7) 2.744(6) 2.360(5) 2.338(5) 2.458(5) 2.346(5) 2.522(7) 2.389(10) 2.679(4) 2.369(4) 2.498(4) 2.370(6) 2.584(4) 2.347(6) 2.395(6) 2.685(7) 2.351(8) 2.418(5) 2.341(6) 2.594(5) 2.370(7) 2.357(5) 2.46(12) 1.497(8) 1.562(5) 1.551(5) 1.552(5) 1.528(5) 1.544(9) 1.532(5) 1.542(6) 1.565(4) 1.525(5) 1.531(6) 1.509(7) 1.54(2)

0.26 0.21 0.18 0.19 0.24 0.14 0.24 0.21 0.24 0.22 0.24 0.18 0.12 0.14 0.12 0.27 0.26 0.22 0.27 0.17 0.27 0.12 0.26 0.21 0.27 0.18 0.26 0.27 0.12 0.26 0.23 0.27 0.15 0.26 0.27 0.22(5) 1.51 1.50 1.53 1.54 1.52 1.48 1.52 1.52 1.49 1.50 1.52 1.53 1.513(17)

2.4416 2.49749 2.61288 2.45843 2.41773 2.35684 2.44556 2.68124 2.38854 2.43777 2.40952 2.38317 2.52426 2.64286 2.35232 2.71125 2.3532 2.33533 2.37375 2.43652 2.5479 2.37385 2.69948 2.33948 2.45993 2.52556 2.34202 2.35593 2.41617 2.58358 2.3348 2.35495 2.3721 2.34212 2.69748 2.46(12) 1.54846 1.55791 1.55205 1.54696 1.54779 1.55814 1.5478 1.55111 1.5488 1.55845 1.54993 1.55008 1.552(4)

occupied, while there exist no hydrogen and oxygen atoms at the other oxygen and hydrogen sites. In hexagonal HAp, the occupancy

factors of both sites are 50%. This indicates the occupational orderdisorder nature of the monoclinichexagonal phase 25084



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Table 8. Minimum Electron Density Obtained by the Combined Technique of Maximum-Entropy Method (MEM) and Minimum Valence-Electron Density Obtained by the First-Principle Density Functional Theory (DFT) Calculations of Hexagonal Hydroxyapatite at 673 K bond

minimum electron density [Å3]

minimum valence-electron density [Å3]

bond length [Å]

bond length [Å]

Ca1O1

0.34

2.4232(11)

0.23

2.42936

Ca1O2

0.26

2.4705(9)

0.21

2.46848

Ca1O3

0.20

2.8272(10)

0.09

2.78168

Ca2O1

0.18

2.7249(13)

0.11

2.75509

Ca2O2 Ca2O3

0.31 0.33

2.3800(10) 2.3652(9)

0.26 0.26

2.35483 2.35971

Ca2O3(2)

0.19

2.5404(12)

0.19

2.47597

Ca2O4

0.24

2.3988(7)

0.25

2.38561

average CaO

0.26(6)

2.52(17)

0.20(7)

2.50(17)

P1O1

1.36

1.5290(14)

1.51

1.54962

P1O2

1.81

1.5323(10)

1.49

1.56031

P1O3

1.52

1.5227(9)

1.50

1.55227

average PO

1.6(2)

1.528(5)

1.50(1)

1.554(3)

Figure 5. Ordering and disordering and charge transfer of hydroxyapatite (HAp). (a,d) Nuclear densities on the bc planes of (a) monoclinic P21/c HAp at x = 0.5 and (b) P63/m hexagonal HAp at x = 0.0, which were obtained by the MEM analysis of neutron powder diffraction data taken in situ at (a) 298 and (d) 673 K, respectively. (a) Monoclinic and (d) hexagonal HAps exhibit the occupational ordering and disordering of oxygen and hydrogen atoms, respectively. Figures (a) and (d) also indicate the orientational ordering and disordering of OH ions (red arrows), respectively. (b,e) Corresponding experimental electron density distributions of (b) P21/c and (e) P63/m HAps obtained by MEM analysis of the synchrotron data ((b) 298 K and (e) 673 K). (c,f) Corresponding theoretical electron density distributions of (c) P21/c and (f) P63/m HAps obtained by the first-principle density functional theory (DFT) calculations. Figures (b,c,e,f) indicate the charge transfer from the H to O atom.

Figure 6. Diffusion mechanism of protons along the c axis in hexagonal hydroxyapatite (HAp). A proton (H1) at z = 0.062 in the initial state (a) bound to an oxygen O1 (z = 0.198) moves along the c axis keeping the O1H1 distance to some degree (b). When the z coordinate of H1 is larger than 1/4, the O1 position changes from z = 0.198 to z = 0.302 (c), which is evidenced by the connected density between these sites. The H1 moves to the next neighbor site (z = 0.438) keeping the O1H1 distance to some degree. In this way, the H1 moves from z = 0.062 to z = 0.438. Similarly, the H2 moves from z = 0.562 (a) to z = 0.938 (d). The connected nuclear density distributions between two hydrogen sites of z = 0.438 and 0.562 indicate ease of proton diffusion between these sites. Consequently, the protons diffuse along the c axis across the cell. A red arrow denotes the OH bond. Blue lines with arrows are possible diffusion paths of the proton.

transition of HAp. The electron density of oxygen atoms bound to a P atom is symmetric in hexagonal HAp, but it is asymmetric in monoclinic HAp (Figures 4e and 4f). This is attributable to the tilting of the PO4 tetrahedron in monoclinic HAp where the tilt angle is estimated to be 2.39(2)° at 298 K. The z coordinate of the Ca2 atom in hexagonal HAp is 1/4, while the corresponding y value of the Ca5 atom in monoclinic HAp is 0.2556(2), leading to the Ca displacement of 0.0385(14) Å from the pseudomirror plane at y = 1/4. These results demonstrate that the hexagonal-tomonoclinic phase transition of HAp is accompanied by (i) the orientational ordering of OH, (ii) occupational ordering of H 25085


The Journal of Physical Chemistry C and O(H) atoms, (iii) tilting of the PO4 tetrahedron, and (iv) displacement of Ca atoms. Thus, the monoclinichexagonal phase transition of HAp has both orderdisorder and displacive natures. The ferroelectricparaelectric phase transition of KTiOPO4 also exhibits both natures.38 3.6. Proton Diffusional Pathway. Next we discuss the mechanism of proton diffusion in HAp. As described above, the hydrogen atom in HAp is a proton and covalently bound to the oxygen O(H) atom, which forms the OH ion. The distance between two proton sites is relatively short (0.86 and 2.60 Å in hexagonal HAp at 673 K, 3.48 Å in monoclinic HAp at 298 K). The distance between hydrogen and oxygen atoms of PO4 in hexagonal HAp is large (>2.9 Å), which indicates that the proton is isolated from PO4. Therefore, the proton can diffuse across the lattice, keeping the OH ion. The atomic displacement parameter of the proton is much higher than those of other atomic species in both monoclinic and hexagonal HAp (U(H) = 0.034(10) Å2 . 0.0050.013 Å2 for other species at 298 K, U(H) = 0.082(9) Å2 . 0.0100.027 Å2 for other species at 673 K, Tables 3 and 4). The nuclear density maps in Figures 4c, 4d, 5a, and 5d also show larger spatial distributions of hydrogen. These results strongly suggest the higher diffusivity of protons compared with other ionic species in HAp, which is consistent with the proton conduction in HAp reported in the literature.3,28 A striking feature of the present nuclear density distribution of hexagonal HAp in Figures 5d and 6 is the short-range diffusion path of protons between two adjacent sites at z = 0.438 and z = 0.562 (and at z = 0.062 and z = 0.938) where the distance between these sites is short (0.86 Å). These distributions also indicate the connected density of oxygen atoms between two adjacent sites at z = 0.198 and z = 0.302 (and at z = 0.698 and z = 0.802), which is regarded as a short-range oxygen diffusion pathway. We propose a possible diffusion pathway of protons across the lattice in Figure 6. (i) The proton H1 at z = 0.062 is bound to an oxygen O1 at z = 0.198 in Figure 6a. (ii) The H1 proton moves from z = 0.062 to 1/4, keeping the OH distance to some degree (Figure 6b). (iii) The oxygen O1 moves from z = 0.198 to 0.302 when the H1 crosses the z = 1/4 position (Figures 6b and 6c). (iv) The H1 proton moves from z = 1/4 to 0.438, keeping the OH distance to some degree (Figures 6c and 6d). (v) The proton moves from z = 0.438 to 0.562 as shown by the short-range diffusion path, forming the new H2O2 bonding shown in Figure 6a. In this way, the change of orientation of the hydroxyl OH ion occurs, accompanied by the proton diffusion from z = 0.062 to 0.562. In Figure 6a, the directions of two OH are down, while they are up in Figure 6d. The H1 and H2 move cooperatively because the H1 and H2 are not able to exist simultaneously at z = 0.438 and z = 0.562, respectively. The proposed mechanism of proton diffusion is consistent with the molecular dynamics simulation reported in the literature.16 Here we have successfully visualized the experimental spatial distributions of proton and O(H).

4. CONCLUSIONS In conclusion, we have successfully addressed the precise chargeand nuclear-density distributions of monoclinic and hexagonal HAp at 298 and 673 K. This work has clearly demonstrated the covalent PO and OH bonds, more ionic CaO bonds, and the charge transfers from P to O atoms and from H to O atoms in HAp. We have also shown that the hexagonalmonoclinic phase transition of HAp is accompanied by the occupational and orientational

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ordering of OH ions, by the tilting of the PO4 tetrahedron, and by the Ca displacement. Diffusion paths of proton and oxygen are visualized along the c axis in hexagonal HAp. It is interesting to point out that the present diffusion pathway of proton along the c axis in hexagonal HAp is similar to the oxygen diffusion pathway along the c axis in hexagonal apatite-type ionic conductor La9.69(Si5.70Mg0.30)O26.24.39 The channel along the c axis in hexagonal apatite-type structured materials such as HAp and La9.69(Si5.70Mg0.30)O26.24 is regarded as a highway of proton and oxide ions. We anticipate that the visualization of chemical bonding and structural disorder of HAp will contribute greatly to our understanding of biominerals, reactions, biological organisms, and the diffusion process in HAp-based proton conductors.

’ ASSOCIATED CONTENT

bS

Supporting Information. Figures S1S3 and Tables S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors would like to thank Prof. K. Ohoyama, Prof. T. Ida, and Mr. M. Ohkawara for their support in the neutron and synchrotron diffraction experiments. We also acknowledge Dr. T. Wakita for the arrangement of ICP measurements. A part of this work was financially supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan, through a Grant-in-Aid for Scientific Research (B) and Challenging Exploratory Research (Nos. 21360318, 23655190) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The synchrotron experiments were done at the BL-4B2 beamline of Photon Factory (PF) of KEK under the project No. 2010G144. This work was carried out under the Joint-use Research Program for Neutron Scattering, Institute for Solid State Physics (ISSP), the University of Tokyo, at the Research Reactor JRR-3, JAEA (Proposal No. 6720, 7770 and 10766). ’ REFERENCES (1) Brown, W. E.; Chow, L. C. Annu. Rev. Mater. Sci. 1976, 6, 213–236. (2) Hench, L. L. J. Am. Ceram. Soc. 1998, 81, 1705–1727. (3) Liu, D.; Savino, K.; Yates, M. Z. Adv. Funct. Mater. 1998, 19, 3941–3947. (4) Posner, A. S.; Perloff, A.; Diorio, A. F. Acta Crystallogr. 1958, 11, 308–309. (5) Kay, M. I.; Young, R. A.; Posner, A. S. Nature 1964, 204, 1050–1052. (6) Elliott, J. C.; Mackie, P. E.; Young, R. A. Science 1973, 180, 1055–1057. (7) Arends, J.; Royce, B. S.; Siegel, J.; Smoluchowski, R. Phys. Lett. A 1968, 27, 720–721. (8) Cant, N. W.; Bett, J. A. S.; Willson, G. R.; Hall, W. K. Spectrochim. Acta A 1971, 27, 425–439. (9) Van Rees, H. B.; Mengeot, M.; Kostiner, E. Mater. Res. Bull. 1973, 8, 1307–1310. (10) Reisner, I.; Klee, W. E. Spectrochim. Acta A 1982, 38 (8), 899–902. 25086



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(11) Hitmi, N.; Chatain, D.; LaCabanne, C.; Dugas, J.; Trombe, J. C.; Rey, C.; Montel, G. Phys. Status Solidi A 1980, 60, 501–506. (12) Hitmi, N.; LaCabanne, C.; Young, R. A. J. Phys. Chem. Solids 1984, 45 (6), 701–708. (13) Hitmi, N.; LaCabanne, C.; Young, R. A. J. Phys. Chem. Solids 1986, 47 (5), 533–546. (14) Suda, H.; Yashima, M.; Kakihana, M.; Yoshimura, M. J. Phys. Chem. 1995, 99, 6752–6754. (15) Takahashi, H.; Yashima, M.; Kakihana, M.; Yoshimura, M. Thermochim. Acta 2001, 371, 53–56. (16) Hochrein, O.; Kniep, R.; Zahn, D. Chem. Mater. 2005, 17, 1978–1981. (17) Coppens, P.; Stevens, E. D. Adv. Quantum Chem. 1977, 10, 1–35. (18) Yashima, M.; Sirikanda, N.; Ishihara, T. J. Am. Chem. Soc. 2010, 132, 2385–2392. (19) de Leeuw, N. H. Chem. Commun. 2001, 2001, 1646–1647. (20) de Leeuw, N. H. Phys. Chem. Chem. Phys. 2002, 4, 3865–3871. (21) de Leeuw, N. H.; Bowe, J. R.; Rabone, J. A. L. Faraday Discuss. 2007, 134, 195–214. (22) Matsunaga, K. J. Chem. Phys. 2008, 128, 245101. (23) Young, R. A. Phys.-Chim. Crystallogr. Apatites d’Inttrtt Biol. 1973, 21–40. (24) Suetsugu, Y.; Ikoma, T.; Tanaka, J. Key Eng. Mater. 2001, 192195, 287–290. (25) Okazaki, M.; Taira, M.; Takahashi, J. Biomaterials 1997, 18, 795–799. (26) Maiti, G. C.; Freund, F. J. Chem. Soc., Dalton Trans. 1981, 1981, 949–955. (27) Nakamura, S.; Takeda, H.; Yamashita, K. J. Appl. Phys. 2001, 89, 5386–5392. (28) Takahashi, H.; Yashima, M.; Kakihana, M.; Yoshimura, M. J. Solid State Inorg. Chem. 1995, 32, 829–935. (29) Yashima, M. J. Am. Ceram. Soc. 2002, 85, 2925–2930. (30) Ohoyama, K.; Kanouchi, T.; Nemoto, K.; Ohashi, M.; Kajitani, T.; Yamaguchi, Y. Jpn. J. Appl. Phys., Part 1 1998, 37, 3319–3326. (31) Izumi, F.; Momma, K. Solid State Phenom, 2007, 130, 15–20. (32) Izumi, F.; Dilanian, R. A. Recent Res. Dev. Phys 2003, 3, 699–726. (33) Momma, K.; Izumi, F. J. Appl. Crystallogr. 2008, 41, 653–658. (34) Toraya, H.; Hibino, H.; Ohsumi, K. J. Synchrotron Radiat. 1996, 3, 75–84. (35) Yashima, M.; Tanaka, M.; Oh-uchi, K.; Ida, T. J. Appl. Crystallogr. 2005, 38, 854–855. (36) Yashima, M.; Oh-uchi, K.; Tanaka, M.; Ida, T. J. Am. Ceram. Soc. 2006, 89, 1395–1399. (37) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (38) Yashima, M.; Komatsu, T. Chem. Commun. 2009, 2009, 1070–1072. (39) Ali, R.; Yashima, M.; Matsushita, Y.; Yoshioka, H.; Ohoyama, K.; Izumi, F. Chem. Mater. 2008, 20, 5203–5208. (40) S€anger, A. T.; Kuhs, W. F. Z. Krist. 1992, 199, 123148.

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