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Substitution mechanism of Zn ions in β-tricalcium phosphate
Physica B 406 (2011) 890–894
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Substitution mechanism of Zn ions in b-tricalcium phosphate Kazuhiko Kawabata a, Tomoyuki Yamamoto b,n, Akihiko Kitada b a b
Department of Holistic Human Sciences, Kwansei Gakuin University, Nishinomiya, Hyogo 662-8501, Japan Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 October 2010 Received in revised form 25 November 2010 Accepted 10 December 2010 Available online 15 December 2010
Zn-doped b-tricalcium phosphate (b-TCP) is synthesized by the solid-state reaction method. The substitution mechanism of Zn ions in b-TCP synthesized here is investigated by carrying out a combination of near-edge X-ray absorption fine structure (NEXAFS) measurements and first-principles calculations. From the results of the present study, the substitution site for Zn ions in b-TCP is successfully determined. & 2010 Elsevier B.V. All rights reserved.
Keywords: Near-edge X-ray absorption fine structure measurement First-principles calculation Bioceramics b-tricalcium phosphate Zinc
1. Introduction Bioceramic materials have been extensively studied because of their potential applications in the medical field, e.g., dentistry and orthopedics. For such applications, bioactive ceramic materials based on hydroxyapatite (HAp) and calcium phosphates are employed to repair bone defects. Among these bioactive materials, tricalcium phosphate (TCP) is a potential candidate for bone substitution. TCP has three types of polymorphs – b, a and a0 phases – depending on the temperature [1]. TCP crystallizes in the b-phase at temperatures below 1400 K, which transfers to the a-phase at 1400 K and it is the a0 -phase above 1740 K. Many attempts have been made to tune the resorption rate of bioceramics implanted for bone reforming by doping them with different types and/or concentrations of trace elements. To understand the influence of dopants, it is essential to know the local environment of the dopants on an atomic scale. Near-edge X-ray absorption fine structure (NEXAFS) analysis is a very powerful tool that enables us to determine the local environment of ultra dilute dopants even at the level of atomic ppm with the aid of the first-principles calculations [2]. This tool has been used for a wide variety of functional materials [3,4]. Recently, the substitution mechanism of Zn ions into HAp has been systematically investigated [5], and we have analyzed the local environment of Mn ions in b-TCP by performing the firstprinciples calculations and NEXAFS measurements [6,7]. Detailed
n
Corresponding author. Tel./fax: +81 3 5286 3317. E-mail address: [email protected] (T. Yamamoto).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.12.022
mechanical and electronic properties of a- and b-TCP [8] were investigated by the first-principles calculations. However, most structural studies on b-TCP, including the analysis of the local environment of trace elements, have been carried out by X-ray and/ or neutron diffraction techniques that are, in a sense, an indirect way of determining the substitution site of dopants. It has been reported that TCP- and HAp-based materials doped with some trace elements such as zinc and magnesium promote excellent bioactivity, which is not the case with the parent materials [9]. Recently, structural studies on Zn-doped b-TCP [10] and Zn- and Si-codoped b-TCP [11] have been conducted by the Rietveld analysis of X-ray and neutron diffraction patterns. In the present study, the substitution mechanism of Zn ions in b-TCP was directly investigated by performing a combination of NEXAFS measurements and first-principles calculations.
2. Experimental procedures Zn-doped b-TCP samples were fabricated by the conventional solidstate reaction method. Commercially available high purity powders of CaHPO4, CaCO3, and ZnO were used as starting materials. To remove the hydrated water, CaHPO4 and CaCO3 powders were dried in air at 473 and 773 K, respectively, for 30 min prior to weighing. Resulting powders were weighed changing the Zn concentrations, x¼0, 0.01, 0.03, 0.05 and 0.1 in Ca3 xZnx(PO4)2, which were mixed and ground in an agate mortar for 30 min and calcined at 1273 K for 6 h in air. High resolution NEXAFS spectra of Zn-doped b-TCP at the Zn K-edge were measured at the BL01B1 in Spring-8, Harima, Japan.
K. Kawabata et al. / Physica B 406 (2011) 890–894
All the measurements were conducted in transmission mode. Incident photon beams were monochromatized using the Si(3 1 1) double-crystal. The Zn K-edge NEXAFS spectrum of ZnO was also measured as a reference.
3. Results and discussion Prior to the NEXAFS measurements, all samples were examined by powder X-ray diffraction (XRD) with y–2y scanning using CuKa irradiation. The resulting XRD patterns of Zn-doped b-TCP powders are shown in Fig. 1, in which the calculated XRD pattern for pure b-TCP (ICSD 410782) is also plotted for comparison. As shown in this figure, no extra peaks appeared in the Zn-doped b-TCP when a Zn concentration, x r0.1 in Ca3 xZnx(PO4)2, was used under the present calcination conditions. These results show that the all samples synthesized here are single-phased b-TCP and that there were no precipitates in the sample specimens due to Zn-doping. To estimate an energetically favorable substitution site for Zn ions in b-TCP, the first-principles calculations were conducted using the plane-wave basis projector augmented wave (PAW) package, vasp [12], in which generalized gradient approximation [13] was employed for the exchange-correlation function. After
891
careful convergence tests with respect to the plane-wave cutoff and the number of k-points, the plane-wave cutoff was set to 400 eV and a 2 2 2 k-point mesh was sampled in the Brillouin-zone for all calculations. There are five crystallographically independent sites, Ca(1)–Ca(5), in the unit cell of b-TCP [14] (Table 1). Prior to the calculations for the Zn-doped models, calculations for pure b-TCP with a Ca vacancy were conducted because the site occupancy of Ca(4) was approximately 0.5, as shown in Table 1. We chose the rhombohedral type of cell with 91 atoms, which was created from a conventional hexagonal unit cell consisting of 273 atoms. Here, we removed one of the Ca ions at the Ca(4) site, which resulted in the site occupancy of Ca(4) being 0.5 because there were two Ca ions in the present rhombohedral cell. This rhombohedral cell is identical to the one determined by the
Table 1 Atomic positions of Ca ions in b-TCP with hexagonal lattice [13]. Element
Site
Ca(1) Ca(2) Ca(3) Ca(4) Ca(5)
18b 18b 18b 6a 6a
x 0.2741 0.3812 0.2734 0.0 0.0
y
Z
0.1382 0.1745 0.1486 0.0 0.0
0.1663 0.0332 0.0611 0.0851 0.2664
Site occupancy 1.0 1.0 1.0 0.43 1.0
100 (a) x = 0.10 50
<111> (1,1,1)
100 (b) x = 0.05
VCa(4)
50
100
Ca(5)vs
Normalized intensity
(c) x = 0.03 50
Ca(1)vs
100
Ca(3)vs (d) x = 0.01
50
Ca(1)os Ca(2)vs
100 (e) x = 0
Ca(4)os
50
Ca(3)os 100
Ca(2)os
(f) calc. 50
Ca(5)os
10
20
30
40
50
60
2θ (deg.) Fig. 1. Observed XRD patterns of Zn-doped and non-doped b-TCP. From top to bottom, x ¼(a) 0.1, (b) 0.05, (c) 0.03, and (d) 0.01; (e) non-doped (x ¼0) in Ca3 xZnx(PO4)2; (f) non-doped b-TCP (ICSD 410782).
(0,0,0) Fig. 2. Schematic illustration of b-TCP with Ca vacancy. Note that only Ca ions are shown in this figure.
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recent first-principles calculations using the hexagonal unit cell [8]. The space group of b-TCP is R3c when there is no Ca vacancy at the Ca(4) site, but it becomes R3 after introduction of the Ca vacancy at the Ca(4) site as in the aforementioned rhombohedral cell. Hence, two crystallographically independent sites for Ca(1),(2),(3),(5) exist (Fig. 2). Hereafter Ca(n) sites (n¼1, 2, 3, 5) at the side closer to the Ca vacancy at Ca(4) are denoted as Ca(n)vs (vacancy side), while those at side opposite the Ca vacancy are denoted as Ca(n)os (n¼1, 2, 3, 4, 5) (opposite side). The calculated cell parameters, a and c, of pure b-TCP ˚ with Ca vacancy at the Ca(4) site are 10.3527 and 37.1498 A, respectively, which quantitatively reproduced the experimental ones ˚ [14], a¼10.3633 and c¼37.2581 A. Next, nine types of Zn-substituted models were constructed, in which the Ca ions at Ca(1, 2, 3, 4, 5)os and Ca(1, 2, 3, 5)vs in the above optimized pure b-TCP cell were replaced by a Zn ion. After geometry optimization of the nine Zn-doped b-TCP models, the relative total electronic energies that correspond to the solution energies of Zn ions in b-TCP, were obtained. The calculated relative
Table 2 Calculated relative total electronic energies of Zn-doped b-TCP. Zn site
DE (eV)
Ca(1)vs Ca(1)os Ca(2)vs Ca(2)os Ca(3)vs Ca(3)os Ca(4)os Ca(5)vs Ca(5)os
1.435 1.615 0.989 1.464 1.140 1.190 0.975 0 0.101
total electronic energies are summarized in Table 2. The total electronic energy for Ca(5)vs substitution was lowest, which indicates that the Ca(5)vs site is the most favorable site in b-TCP for Zn substitutions. The observed Zn K-edge NEXAFS spectra of Zn-doped b-TCP are shown in Fig. 3 together with that of ZnO. The spectral fine structures of Zn-doped b-TCP with different concentrations of Zn ions showed almost the same features but they were clearly distinguishable from ZnO and Zn-doped HAp [5]. These results indicate that the local environment of Zn ions in b-TCP are nearly identical even when the Zn concentrations, x, vary from 0.01 to 0.1 but that they differ from that in ZnO. It is very difficult to determine the local structure of doped ions using the conventional fingerprint type analysis for this type of doped ion. Accordingly, the first-principles calculations were mandatory to obtain the theoretical Zn K-edge NEXAFS, i.e., theoretical fingerprints, of the Zn ions substituted in b-TCP. In these calculations, the fullpotential augmented plane-wave plus local orbital (APW+lo) package, WIEN2k [15], was employed. The muffin-tin radii, RMT, of Ca and Zn, and P and O were 1.8 and 1.4 a.u., respectively, and the product of RMT and Kmax, which corresponds to the plane-wave cutoff, was set to 5.0 (a.u. Ry1/2) for all calculations. A 2 2 2 k-point mesh was sampled in the Brillouin-zone. The core-hole effect was fully introduced by removing the core electron from the Zn K-shell and putting an additional electron at the bottom of the conduction band, which approximately corresponds to the final state of the X-ray absorption of interest. Theoretical spectral profiles were obtained from the product of the projected partial density of state of Zn p-component in the conduction band and the radial part of the transition probability within the electricdipole-allowed transition. The calculated spectra were broadened using the Gaussian function of G ¼1.67 eV full width at half maximum, which corresponds to the core life-time of the Zn K-shell [16]. The transition energy was calculated based on the difference in total electronic energies between initial (ground) and final (core-holed) states.
(a) expt. d
c
e
a
f
x = 0.01 Intensity (arb. units)
Relative Intensity (arb. units)
b
x = 0.03
x = 0.05
b (b) calc. d
a c
x = 0.1
e
f
ZnO 9650
9650
9660
9670 Energy (eV)
9680
Fig. 3. Observed Zn K-edge NEXAFS spectra of Zn-doped b-TCP, Ca1 xZnx(PO4)2. From top to bottom, x ¼(a) 0.1, (b) 0.05, (c) 0.03, and (d) 0.01; (e) ZnO.
9660
9670 Energy (eV)
9680
9690
Fig. 4. Comparison between (a) observed and (b) calculated NEXAFS spectra of ZnO at Zn K-edge. The transition energy of the calculated NEXAFS spectrum is corrected by DE ¼ 34 eV (DE/E¼ 0.3%).
K. Kawabata et al. / Physica B 406 (2011) 890–894
A B C
expt.
expt.
D
D
E
calc.
Ca(5)os
Intensity (arb. units)
Ca(5)vs Intensity (arb. units)
A B C
E
calc.
Ca(3)vs
Ca(2)vs
Ca(1)vs
9650
893
Ca(4)os
Ca(3)os
Ca(2)os
9660
9670
9680
Energy (eV) Fig. 5. Comparison between (a) observed and (b) calculated Zn K-edge NEXAFS spectra of Zn-doped b-TCP. Calculated NEXAFS spectra are for the Zn ions substituted at Ca(1)vs–(5)vs, which are shifted by DE¼ 34 eV (DE/E ¼0.3%).
Ca(1)os 9650
9660 9670 Energy (eV)
9680
Fig. 6. Same as Fig. 5 but Zn ions substituted at Ca(1)os–(5)os.
Prior to comparison of the observed and calculated NEXAFS spectra of Zn-doped b-TCP, the validity of the present NEXAFS calculation was examined by comparing the calculated Zn K-edge spectrum of ZnO to the experimental one, as shown in Fig. 4. This NEXAFS calculation was conducted using the 3 3 2 supercell of a wurtzite structured unit cell of ZnO consisting of 72 atoms. The same RMT values for Zn and O and RMTKmax were used for the Zn-doped b-TCP. The observed spectral fine structure of the Zn K-edge NEXAFS of ZnO was quantitatively well reproduced by the present calculations when the transition energy was corrected by DE¼ 34 eV (DE/E ¼0.35%). The calculated NEXAFS spectra of Zn ions substituted for nine different Ca sites, Ca(1, 2, 3, 4, 5)os and Ca(1, 2, 3, 5)vs sites in b-TCP, are shown in Figs. 5 and 6, respectively, in which the transition energy was corrected by the same amount of energy as for ZnO, i.e., DE¼ 34 eV. Each of the calculated spectra shows different fine structures that vary depending on the local environments of the Zn ions in b-TCP. The calculated NEXAFS spectrum of the Ca(5)vs substitution model, which was the energetically most favorable model estimated by the planewave basis first-principles calculations, shows the best agreement with the experimental fine structure.
4. Summary We synthesized Zn-doped b-TCP by the conventional solid-state reaction method and investigated the substitution mechanism of Zn ions in b-TCP by performing (1) XRD measurements, (2) solution energy calculations based on the first-principles calculations using a plane-wave basis, (3) NEXAFS measurements, and (4) firstprinciples NEXAFS calculations. From the above results, we can conclude that Zn ions are substituted at the Ca(5)vs site in b-TCP under the present calcination conditions. This type of combined analysis of the local environments of doped ions is very effective and can be used for the analysis of other trace elements in bioceramic materials.
Acknowledgement Zn-K NEXAFS measurements were conducted at the BL01B1 in Spring-8 with the approval of the Japan Radiation Research Institute (JASRI) (proposal no. 2008A1274).
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References [1] M. Mathew, L.W. Schroeder, B. Dickens, W.E. Brown, Acta Crystallogr. B 33 (1977) 1325. [2] I. Tanaka, T. Mizoguchi, M. Matsui, S. Yoshioka, H. Adachi, T. Yamamoto, T. Okajima, M. Umesaki, W.Y. Ching, Y. Inoue, M. Mizuno, H. Araki, Y. Shirai, Nat. Mater. 2 (2003) 541. [3] I. Tanaka, T. Mizoguchi, T. Yamamoto, J. Am. Ceram. Soc. 88 (2005) 2013. [4] T. Yamamoto, Y. Kawashima, Y. Kusakabe, S. Matsuda, Y. Mizuoka, Y. Nakade, T. Okajima, J. Phys.: Condens. Matter 21 (2009) 104211. [5] K. Matsunaga, H. Murata, T. Mizoguchi, A. Nakahira, Acta Biomater. 6 (2010) 2289. [6] K. Kawabata, H. Sato, T. Yamamoto, J. Ceram. Soc. Jpn. 116 (2008) 108. [7] K. Kawabata, H. Sato, T. Yamamoto, Arch. Bioceram. Res. 7 (2007) 181.
[8] L. Liang, P. Rulis, W.Y. Ching, Acta Biomater. 6 (2010) 2763. [9] H. Kawamura, A. Ito, S. Miyakawa, P. Layrolle, K. Ojima, H. Naito, N. Ichinose, T. Tateishi, J. Biomed. Mater. Res. 50 (2000) 184. [10] S. Kanan, F. Goetz-Neunhoeffer, J. Neubauer, J.M.F. Ferreira, J. Am. Ceram. Soc. 92 (2009) 1592. [11] Z. Wei, M. Akinc, J. Am. Ceram. Soc. 90 (2007) 2709. ¨ [12] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [13] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. [14] M. Yashima, A. Sakai, T. Kamiyama, A. Hoshikawa, J. Solid State Chem. 175 (2003) 272. [15] P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbital Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universitat Wien, Austria, 2001. ISBN 3-9501031-1-2). [16] M.O. Krause, J.H. Oliver, J. Phys. Chem. Ref. Data 8 (1979) 329.
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Physica B journal homepage: www.elsevier.com/locate/physb
Substitution mechanism of Zn ions in b-tricalcium phosphate Kazuhiko Kawabata a, Tomoyuki Yamamoto b,n, Akihiko Kitada b a b
Department of Holistic Human Sciences, Kwansei Gakuin University, Nishinomiya, Hyogo 662-8501, Japan Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 October 2010 Received in revised form 25 November 2010 Accepted 10 December 2010 Available online 15 December 2010
Zn-doped b-tricalcium phosphate (b-TCP) is synthesized by the solid-state reaction method. The substitution mechanism of Zn ions in b-TCP synthesized here is investigated by carrying out a combination of near-edge X-ray absorption fine structure (NEXAFS) measurements and first-principles calculations. From the results of the present study, the substitution site for Zn ions in b-TCP is successfully determined. & 2010 Elsevier B.V. All rights reserved.
Keywords: Near-edge X-ray absorption fine structure measurement First-principles calculation Bioceramics b-tricalcium phosphate Zinc
1. Introduction Bioceramic materials have been extensively studied because of their potential applications in the medical field, e.g., dentistry and orthopedics. For such applications, bioactive ceramic materials based on hydroxyapatite (HAp) and calcium phosphates are employed to repair bone defects. Among these bioactive materials, tricalcium phosphate (TCP) is a potential candidate for bone substitution. TCP has three types of polymorphs – b, a and a0 phases – depending on the temperature [1]. TCP crystallizes in the b-phase at temperatures below 1400 K, which transfers to the a-phase at 1400 K and it is the a0 -phase above 1740 K. Many attempts have been made to tune the resorption rate of bioceramics implanted for bone reforming by doping them with different types and/or concentrations of trace elements. To understand the influence of dopants, it is essential to know the local environment of the dopants on an atomic scale. Near-edge X-ray absorption fine structure (NEXAFS) analysis is a very powerful tool that enables us to determine the local environment of ultra dilute dopants even at the level of atomic ppm with the aid of the first-principles calculations [2]. This tool has been used for a wide variety of functional materials [3,4]. Recently, the substitution mechanism of Zn ions into HAp has been systematically investigated [5], and we have analyzed the local environment of Mn ions in b-TCP by performing the firstprinciples calculations and NEXAFS measurements [6,7]. Detailed
n
Corresponding author. Tel./fax: +81 3 5286 3317. E-mail address: [email protected] (T. Yamamoto).
0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.12.022
mechanical and electronic properties of a- and b-TCP [8] were investigated by the first-principles calculations. However, most structural studies on b-TCP, including the analysis of the local environment of trace elements, have been carried out by X-ray and/ or neutron diffraction techniques that are, in a sense, an indirect way of determining the substitution site of dopants. It has been reported that TCP- and HAp-based materials doped with some trace elements such as zinc and magnesium promote excellent bioactivity, which is not the case with the parent materials [9]. Recently, structural studies on Zn-doped b-TCP [10] and Zn- and Si-codoped b-TCP [11] have been conducted by the Rietveld analysis of X-ray and neutron diffraction patterns. In the present study, the substitution mechanism of Zn ions in b-TCP was directly investigated by performing a combination of NEXAFS measurements and first-principles calculations.
2. Experimental procedures Zn-doped b-TCP samples were fabricated by the conventional solidstate reaction method. Commercially available high purity powders of CaHPO4, CaCO3, and ZnO were used as starting materials. To remove the hydrated water, CaHPO4 and CaCO3 powders were dried in air at 473 and 773 K, respectively, for 30 min prior to weighing. Resulting powders were weighed changing the Zn concentrations, x¼0, 0.01, 0.03, 0.05 and 0.1 in Ca3 xZnx(PO4)2, which were mixed and ground in an agate mortar for 30 min and calcined at 1273 K for 6 h in air. High resolution NEXAFS spectra of Zn-doped b-TCP at the Zn K-edge were measured at the BL01B1 in Spring-8, Harima, Japan.
K. Kawabata et al. / Physica B 406 (2011) 890–894
All the measurements were conducted in transmission mode. Incident photon beams were monochromatized using the Si(3 1 1) double-crystal. The Zn K-edge NEXAFS spectrum of ZnO was also measured as a reference.
3. Results and discussion Prior to the NEXAFS measurements, all samples were examined by powder X-ray diffraction (XRD) with y–2y scanning using CuKa irradiation. The resulting XRD patterns of Zn-doped b-TCP powders are shown in Fig. 1, in which the calculated XRD pattern for pure b-TCP (ICSD 410782) is also plotted for comparison. As shown in this figure, no extra peaks appeared in the Zn-doped b-TCP when a Zn concentration, x r0.1 in Ca3 xZnx(PO4)2, was used under the present calcination conditions. These results show that the all samples synthesized here are single-phased b-TCP and that there were no precipitates in the sample specimens due to Zn-doping. To estimate an energetically favorable substitution site for Zn ions in b-TCP, the first-principles calculations were conducted using the plane-wave basis projector augmented wave (PAW) package, vasp [12], in which generalized gradient approximation [13] was employed for the exchange-correlation function. After
891
careful convergence tests with respect to the plane-wave cutoff and the number of k-points, the plane-wave cutoff was set to 400 eV and a 2 2 2 k-point mesh was sampled in the Brillouin-zone for all calculations. There are five crystallographically independent sites, Ca(1)–Ca(5), in the unit cell of b-TCP [14] (Table 1). Prior to the calculations for the Zn-doped models, calculations for pure b-TCP with a Ca vacancy were conducted because the site occupancy of Ca(4) was approximately 0.5, as shown in Table 1. We chose the rhombohedral type of cell with 91 atoms, which was created from a conventional hexagonal unit cell consisting of 273 atoms. Here, we removed one of the Ca ions at the Ca(4) site, which resulted in the site occupancy of Ca(4) being 0.5 because there were two Ca ions in the present rhombohedral cell. This rhombohedral cell is identical to the one determined by the
Table 1 Atomic positions of Ca ions in b-TCP with hexagonal lattice [13]. Element
Site
Ca(1) Ca(2) Ca(3) Ca(4) Ca(5)
18b 18b 18b 6a 6a
x 0.2741 0.3812 0.2734 0.0 0.0
y
Z
0.1382 0.1745 0.1486 0.0 0.0
0.1663 0.0332 0.0611 0.0851 0.2664
Site occupancy 1.0 1.0 1.0 0.43 1.0
100 (a) x = 0.10 50
<111> (1,1,1)
100 (b) x = 0.05
VCa(4)
50
100
Ca(5)vs
Normalized intensity
(c) x = 0.03 50
Ca(1)vs
100
Ca(3)vs (d) x = 0.01
50
Ca(1)os Ca(2)vs
100 (e) x = 0
Ca(4)os
50
Ca(3)os 100
Ca(2)os
(f) calc. 50
Ca(5)os
10
20
30
40
50
60
2θ (deg.) Fig. 1. Observed XRD patterns of Zn-doped and non-doped b-TCP. From top to bottom, x ¼(a) 0.1, (b) 0.05, (c) 0.03, and (d) 0.01; (e) non-doped (x ¼0) in Ca3 xZnx(PO4)2; (f) non-doped b-TCP (ICSD 410782).
(0,0,0) Fig. 2. Schematic illustration of b-TCP with Ca vacancy. Note that only Ca ions are shown in this figure.
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K. Kawabata et al. / Physica B 406 (2011) 890–894
recent first-principles calculations using the hexagonal unit cell [8]. The space group of b-TCP is R3c when there is no Ca vacancy at the Ca(4) site, but it becomes R3 after introduction of the Ca vacancy at the Ca(4) site as in the aforementioned rhombohedral cell. Hence, two crystallographically independent sites for Ca(1),(2),(3),(5) exist (Fig. 2). Hereafter Ca(n) sites (n¼1, 2, 3, 5) at the side closer to the Ca vacancy at Ca(4) are denoted as Ca(n)vs (vacancy side), while those at side opposite the Ca vacancy are denoted as Ca(n)os (n¼1, 2, 3, 4, 5) (opposite side). The calculated cell parameters, a and c, of pure b-TCP ˚ with Ca vacancy at the Ca(4) site are 10.3527 and 37.1498 A, respectively, which quantitatively reproduced the experimental ones ˚ [14], a¼10.3633 and c¼37.2581 A. Next, nine types of Zn-substituted models were constructed, in which the Ca ions at Ca(1, 2, 3, 4, 5)os and Ca(1, 2, 3, 5)vs in the above optimized pure b-TCP cell were replaced by a Zn ion. After geometry optimization of the nine Zn-doped b-TCP models, the relative total electronic energies that correspond to the solution energies of Zn ions in b-TCP, were obtained. The calculated relative
Table 2 Calculated relative total electronic energies of Zn-doped b-TCP. Zn site
DE (eV)
Ca(1)vs Ca(1)os Ca(2)vs Ca(2)os Ca(3)vs Ca(3)os Ca(4)os Ca(5)vs Ca(5)os
1.435 1.615 0.989 1.464 1.140 1.190 0.975 0 0.101
total electronic energies are summarized in Table 2. The total electronic energy for Ca(5)vs substitution was lowest, which indicates that the Ca(5)vs site is the most favorable site in b-TCP for Zn substitutions. The observed Zn K-edge NEXAFS spectra of Zn-doped b-TCP are shown in Fig. 3 together with that of ZnO. The spectral fine structures of Zn-doped b-TCP with different concentrations of Zn ions showed almost the same features but they were clearly distinguishable from ZnO and Zn-doped HAp [5]. These results indicate that the local environment of Zn ions in b-TCP are nearly identical even when the Zn concentrations, x, vary from 0.01 to 0.1 but that they differ from that in ZnO. It is very difficult to determine the local structure of doped ions using the conventional fingerprint type analysis for this type of doped ion. Accordingly, the first-principles calculations were mandatory to obtain the theoretical Zn K-edge NEXAFS, i.e., theoretical fingerprints, of the Zn ions substituted in b-TCP. In these calculations, the fullpotential augmented plane-wave plus local orbital (APW+lo) package, WIEN2k [15], was employed. The muffin-tin radii, RMT, of Ca and Zn, and P and O were 1.8 and 1.4 a.u., respectively, and the product of RMT and Kmax, which corresponds to the plane-wave cutoff, was set to 5.0 (a.u. Ry1/2) for all calculations. A 2 2 2 k-point mesh was sampled in the Brillouin-zone. The core-hole effect was fully introduced by removing the core electron from the Zn K-shell and putting an additional electron at the bottom of the conduction band, which approximately corresponds to the final state of the X-ray absorption of interest. Theoretical spectral profiles were obtained from the product of the projected partial density of state of Zn p-component in the conduction band and the radial part of the transition probability within the electricdipole-allowed transition. The calculated spectra were broadened using the Gaussian function of G ¼1.67 eV full width at half maximum, which corresponds to the core life-time of the Zn K-shell [16]. The transition energy was calculated based on the difference in total electronic energies between initial (ground) and final (core-holed) states.
(a) expt. d
c
e
a
f
x = 0.01 Intensity (arb. units)
Relative Intensity (arb. units)
b
x = 0.03
x = 0.05
b (b) calc. d
a c
x = 0.1
e
f
ZnO 9650
9650
9660
9670 Energy (eV)
9680
Fig. 3. Observed Zn K-edge NEXAFS spectra of Zn-doped b-TCP, Ca1 xZnx(PO4)2. From top to bottom, x ¼(a) 0.1, (b) 0.05, (c) 0.03, and (d) 0.01; (e) ZnO.
9660
9670 Energy (eV)
9680
9690
Fig. 4. Comparison between (a) observed and (b) calculated NEXAFS spectra of ZnO at Zn K-edge. The transition energy of the calculated NEXAFS spectrum is corrected by DE ¼ 34 eV (DE/E¼ 0.3%).
K. Kawabata et al. / Physica B 406 (2011) 890–894
A B C
expt.
expt.
D
D
E
calc.
Ca(5)os
Intensity (arb. units)
Ca(5)vs Intensity (arb. units)
A B C
E
calc.
Ca(3)vs
Ca(2)vs
Ca(1)vs
9650
893
Ca(4)os
Ca(3)os
Ca(2)os
9660
9670
9680
Energy (eV) Fig. 5. Comparison between (a) observed and (b) calculated Zn K-edge NEXAFS spectra of Zn-doped b-TCP. Calculated NEXAFS spectra are for the Zn ions substituted at Ca(1)vs–(5)vs, which are shifted by DE¼ 34 eV (DE/E ¼0.3%).
Ca(1)os 9650
9660 9670 Energy (eV)
9680
Fig. 6. Same as Fig. 5 but Zn ions substituted at Ca(1)os–(5)os.
Prior to comparison of the observed and calculated NEXAFS spectra of Zn-doped b-TCP, the validity of the present NEXAFS calculation was examined by comparing the calculated Zn K-edge spectrum of ZnO to the experimental one, as shown in Fig. 4. This NEXAFS calculation was conducted using the 3 3 2 supercell of a wurtzite structured unit cell of ZnO consisting of 72 atoms. The same RMT values for Zn and O and RMTKmax were used for the Zn-doped b-TCP. The observed spectral fine structure of the Zn K-edge NEXAFS of ZnO was quantitatively well reproduced by the present calculations when the transition energy was corrected by DE¼ 34 eV (DE/E ¼0.35%). The calculated NEXAFS spectra of Zn ions substituted for nine different Ca sites, Ca(1, 2, 3, 4, 5)os and Ca(1, 2, 3, 5)vs sites in b-TCP, are shown in Figs. 5 and 6, respectively, in which the transition energy was corrected by the same amount of energy as for ZnO, i.e., DE¼ 34 eV. Each of the calculated spectra shows different fine structures that vary depending on the local environments of the Zn ions in b-TCP. The calculated NEXAFS spectrum of the Ca(5)vs substitution model, which was the energetically most favorable model estimated by the planewave basis first-principles calculations, shows the best agreement with the experimental fine structure.
4. Summary We synthesized Zn-doped b-TCP by the conventional solid-state reaction method and investigated the substitution mechanism of Zn ions in b-TCP by performing (1) XRD measurements, (2) solution energy calculations based on the first-principles calculations using a plane-wave basis, (3) NEXAFS measurements, and (4) firstprinciples NEXAFS calculations. From the above results, we can conclude that Zn ions are substituted at the Ca(5)vs site in b-TCP under the present calcination conditions. This type of combined analysis of the local environments of doped ions is very effective and can be used for the analysis of other trace elements in bioceramic materials.
Acknowledgement Zn-K NEXAFS measurements were conducted at the BL01B1 in Spring-8 with the approval of the Japan Radiation Research Institute (JASRI) (proposal no. 2008A1274).
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