Beta-tri-calcium phosphate (β-TCP) materials have gained a great deal of research considerations in biomaterial area due to their excellent biocompatibility and identical chemical compositions to the natural teeth and bones. Therefore, the β-TCP compound can be used as coatings, cement and composites as well as biocompatible ceramics for medical and dental applications. Electronic and optical properties for β-TCP compound have been investigated using density functional theory (DFT). For the calculations, we used full potential linear augmented plane wave method (FPLAPW), within three types of approximations along with local density approximations (LDA), generalized gradient approximations (GGA) and Modified Becke-Johnson (mBJ) to get the effect of the exchange and correlation in our calculations to get an accurate results. The computed band gap values for (β-TCP) compound using LDA, GGA, and mBJ-GGA approximations are 5.5 eV, 5.9 eV and 6.8 eV respectively. This is also predicted that the chemical bonding in this compound is a kind of combination of covalent and ionic character that is in a line with the experimental findings. The optical parameter, static dielectric constant ε1(0) reaches the values of 3.23681 (eV) at 0 GPa for the β-TCP compound. The obtained results are of vital nature for rising the quality of the electronic and optical properties of this material, and provide more evidence to fabricate novel Beta-Tri-calcium phosphate biomaterials for medical and dental applications

Bakheet, Ahmed M. A.

Mat Isa, Ahmad Radzi

Saeed, Mohammad Alam

Sahnoun, Riadh

Universiti Teknologi Malaysia Institutional Repository

Jurnal TeknologiFull PaperTh e o r e t ic a l  In v e s t ig a t io n s  o f  P - t r ic a l c iu m  Ph o s p h a t e  B io m a t e r ia l s : dft in s ig h tA. M. A. Bakheeta, M. A. Saeeda*, A. R. M. Isaa , R. SahnounbaDepartment of Physics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia bIbnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, MalaysiaArticle historyReceived 10 February 2015 Received in revised form 10 Novem ber 2015 A cce p te d  12 Novem ber 2015*Corresponding author saeed@utm.myGraphical abstract AbstractBeta-tri-calcium phosphate (|3-TCP) materials have gained a great deal of research considerations in biomaterial area due to their excellent biocompatibility and identical chem ical compositions to the natural teeth and bones. Therefore, the |3-TCP com pound can  be used as coatings, cem ent and composites as well as biocompatible ceram ics for m edical and dental applications. Electronic and optical properties for |3-TCP com pound have been investigated using density functional theory (DFT). For the calculations, we used full potential linear augm ented plane w ave method (FPLAPW), within three types of approximations along with local density approximations (LDA), generalized gradient approximations (GGA) and Modified Becke-Johnson (mBJ) to get the effect of the exchange and correlation in our calculations to get an accurate  results. The computed band gap  values for (|3-TCP) com pound using LDA, G G A , and m BJ-GGA approximations are 5.5 eV, 5.9 eV and 6.8 eV respectively. This is also predicted that the chem ical bonding in this com pound is a kind of combination of covalent and ionic character that is in a line with the experimental findings. The optical parameter, static dielectric constant £i (0) reaches the values of 3.23681 (eV) at 0 G Pa for the |3-TCP compound. The obtained results are of vital nature for rising the quality of the electronic and optical properties of this material, and provide more evidence to fabricate novel Beta-Tri-calcium phosphate biomaterials for medical and dental applications.Keywords: Density functional theory; tri-calcium phosphate; biomaterial, electronic properties; optical properties.AbstrakBahan Beta-tri-kalsium fosfat (|3-TCP) telah m endapat banyak pertimbangan penyelidikan dalam  bidang biobahan kerana keserasian bio yang cem erlang dan komposisi kimia yang serupa kepada gigi dan tulang secara semula jadi. Oleh itu, sebatian |3-TCP boleh digunakan sebagai salutan, simen dan komposit serta seramik keserasian bio untuk kegunaan perubatan dan pergigian. Sifat elektronik dan optik sebatian |3-TCP telah dikaji m enggunakan teori fungsional ketumpatan (DFT). Untuk pengiraan, kita m enggunakan potensi penuh kaedah gelom bang satah linear diperkukuhkan (FP LAPW), dalam  tiga jenis an ggaran  bersam a-sam a dengan anggaran ketumpatan setempat (LDA), an ggaran  kecerunan umum (GGA) dan Ubahsuai Becke- Johnson (MBJ) untuk m endapatkan kesan pertukaran dan korelasi dalam  pengiraan kami untuk m endapatkan keputusan yang tepat. Nilai jurang jalur dikira untuk sebatian (|3-TCP) m enggunakan LDA, G G A  dan M BJ-GGA an ggaran  ad alah 5.5 eV, 5.9 eV dan 6.8 eV masing-masing. Ini juga meramalkan bahaw a ikatan kimia dalam  sebatian ini adalah sejenis gab ungan kovalen dan sifat ionik yang selaras dengan dapatan eksperimen. Parameter optik, pem alar dielektrik statik £](0) m encapai nilai-nilai 3.23681 (eV) p a d a  078: 3-2 (2016) 159-164 | www.jurnalteknologi.utm.my | elSSN 2180-3722 |160 A. M. A. Bakheet et al. / Jurnal Teknologi (Sciences & Engineering) 78: 3-2 (2016) 159-164G Pa untuk sebatian |3-TCP. Keputusan yang diperolehi ad alah sifat penting untuk meningkat kualiti sifat elektronik dan optik bahan ini, dan m enyediakan lebih banyak bukti untuk merekabentuk Beta-Tri-kalsium fosfat biobahan yang baru untuk aplikasi perubatan dan pergigian.Kata kunci: Teori Kefungsian ketumpatan, tri-kalsium posfat, sifat elektronik dan sifat optik bio-bahan© 2016 Penerbit UTM Press. All rights reserved1.0 INTRODUCTIONDuring the last fifty years, a great progress has been m ade in material and m edical sciences areas to improve the calcium  phosphate ceram ic properties to use it for repairing and rebuilding the dam aged  part (s) of the skeletal bones [1]. Therefore, the developm ent of calcium  phosphate bio-ceram ic has been recognized as a major addition to the m edical science applications [2]. Calcium  phosphate biomaterials have been regarded as a potential bone replacem ent due to their mineral composition similar to the natural bones and teeth [3, 4]. Therefore, calcium  phosphate biomaterials are extensively used in bone replacement, bone augmentation, as well as in bone repairing and reformation [5]. The crystal structure of p>-TCP is rhombohedral with a sp ace  group of (R3c, Z = 21), which is shown in Fig. 1. (3-TCP is formed at low temperature, and it is stable under 1120 C0 [6], which makes it as essential constituent elements for living teeth and bones [7].Beta-tri-calcium phosphate has important applications when it is used as the synthetic material in bone replacem ent for surgical therapy, in order to fix the bone injury using maxillofacial surgeons and orthopedic surgeons [8]. However, some researchers reported that, doping p>-TCP com pound with Zinc (Zn) element has a high solubility for the bone cells when it is used as bone substitution [9]. Another experimental study reported that, a doping p>-TCP com pound with Zn element ch an ged  the p>-TCP structure; thereby the electronic and optical properties are ch an ged  as well. This means, the substitution of Zn decreases the crystallinity and destabilizes the structure of p>-TCP com pound [10], which has a negative effect on (3-TCP properties when it is used as bone and teeth replacem ent. Therefore, in this study we have used theoretical investigations, to ca lcu late  electronic and optical properties of the pure p>-TCP com pound in the R3c crystal structure of the experimental lattice constants at ground state energy. This study will provide more understanding and a clear picture of this com pound, and supports researchers to design a com patible p>-TCP biomaterial that can  be used in several clinical applications.For the electronic and optical properties calculations, we used full potential linear augm ented plane w ave method (FPLAPW), within (LDA), (GGA)and (mBJ-GGA) approximations as implemented into WIEN2k P ackage  [11].The materials that are used for implants purposes should possess special characteristics such as, high biocompatibility, good solidity and adequate resistance to the corrosion defects [7]. In this regards, P-TCP com pound is considered as essential constituent elements for living teeth and bones. Indeed, it plays an important role in graft issues, which is m ade it as uniquely biocom patible ceram ics in m edical and dental applications [12].Figure 1 Crystal structure of pure Beta-Tri-calcium phosphate (|3-TCP) compound.161 A. M. A. Bakheet et al. / Jurnal Teknologi (Sciences & Engineering) 78: 3-2 (2016) 159-1642.0 COMPUTATIONAL METHODOLOGYTheoretical calculations that em ploy periodic boundary conditions are an effective w ay to model the physical properties of solid materials at the atom ic level as a com plem ent to the experimental studies [13]. In this respects, we performed our calculations using a self-consistent schem e by solving the Kohn- Sham equations using density functional theory (DFT) along with local density approximations (LDA), generalized gradient approximations (GGA) [14] and Modified Becke-Johnson method (mBJ-GGA) as implemented into WIEN2k p a ck a ge  [11].The value of RMT^max =  3, is adopted to ach ieve self-consistence field (scf) co nvergence for the electronic and optical calculations, where RMT is the smallest atom ic radius in a unit cell, and Kmax is the m agnitude of the maximum value of k-vector in the plane w ave expansion. The number of 1500 k-points is used as input parameter for the self-consistent charge density determination, in the irreducible symmetry w edge of the Brillion Zone (BZ) [15]. The energy co nvergence of 10-6 Ryd is chosen for the cut-off energy. In addition, we have used the values of muffin-tin radii of 2.2, 1.8, and 1.07 atom ic units (a.u) for C a , P, and O  elements, respectively.The electronic and optical properties calculations are investigated with the above mentioned com putational parameters, using experimental lattice constants of the pure p>-TCP com pound, which are taken from reference [16], and our above-mentioned computation details to get the relaxed structure of the P-TCP com pound. Then, we have used it to perform our electronic and optical properties calculations using LDA, G G A , and m BJ-G G A approximations.3.0 RESULTS AND DISCUSSION3.1 Electronic PropertiesWe have investigated the electronic band structure calculations for p>-TCP com pound, and the results are displayed in Fig. 2. It is clear from Fig. 2 that, the Fermi level is set at 0 eV  on energy scale, conduction band minima (CBM) and valence  band maxima (VBM) are located at the central symmetry (C) line of the Brillion zone, which shows the direct band g a p  nature for the full range of concentration.The calcu lated  band g a p  values using m BJ-G G A method has high value com pared to those using LDA and G G A  approximations. The obtained band ga p  value with G G A  method is quite closer to that one com puted by m BJ-GGA method. Fig. 2 shows the calcu lated  band g a p  plot for a p>-TCP com pound with values of 5.2 eV, 5.9 eV and 6.8 eV using LDA, G G A , m BJ-G G A approximations, respectively.We reported the results of calcu lated  band ga p  values for the p>-TCP com pound of other studies tomake a comparison with our current work. Xilin and Lazaro calculated the band g a p  value (2.4eV) for a P-TCP com pound using density functional theory calculations along with Perdew-Wang (PWC) exchange-correlation [10]. Whereas L. Liange, P. Rulis and W.Y. Ching in 2010, performed DFT study to calcu late  the band ga p  value (5.25 eV) for p>-TCP com pound [17], this result is closer to our calculated band value using G G A  approximation.In order to get more understanding of the nature of electronic band structure, we have also calculated the projected density of states (PDOS) and total density of states (TDOS) for a p>-TCP com pound using LDA, G G A  and m BJ-G G A approximations. The results of calculated TDOS and PDOS for p>-TCP com pound are presented in Fig. 3, 4 and 5 using LDA, G G A , and m BJ-GGA methods, respectively. In Fig. 3, 4 and 5, the total density of states of p>-TCP com pound are shown between -23.6 eV and 15 eV. For the projected density of states, the p-state of C a ^ n d  Ca2 atoms are participated into the total Dos of pure p>-TCP, in the energy range of -18 eV to -20 eV. While for P atom, the S and P states are contributed into the total DOS started at -21 eV (LDA), -17eV (GGA), and 23eV (mBJ- G G A), and ended at 15.0 eV. The S state of Oi is participated into TDOS from -20 eV to 12.5 eV, from - 20 eV to -18.0 eV and from -25 eV to 13.5 eV for the LDA, G G A , m BJ-G G A approximations, respectively.Figure 2 Structures of the |3-T CP com pound with LDA, G G A , and m BJ-GGA calculations.The s and p-states of O2 element are participated into the TDOS from -21 eV to 12 eV (LDA), from -21.5 eV to 13.0 eV (GGA), and from -23 eV to 14.0 eV (mBJ-GGA) approximations. The p-state of C a ^ n d  Ca2 has high162 A. M. A. Bakheet et al. / Jurnal Teknologi (Sciences & Engineering) 78: 3-2 (2016) 159-164contribution into the TDOS, which is shown in Fig. 3 and Fig. 4, while in Fig. 5, both s &p-states of C a ^ n d  Ca2 have high contribution into the TDOS.LDAmBJ-GGA>o"BoraWCO0' '  ^ — Tola l DOS:: fill AM/i. :I 1------- Ca1 ^------- Ca1 p------- 0a2s------- Ca2p- L 1 M aJUL-------- P s•PI ^ 1------- 01 $-------01 pT . M i  ■ i  *4 ----------T---------1--------02  s------- 02  p-20 -15 -10 -5 0 Energy (eV)10 15 20Figure 3 Density of States (DOS) of the |3-TCP com pound with LDA calculations.GGASSQ 0.2 0.0 1.5 1.0 0.5 0.0 1.2 0.9 0.6 0.3 0.0i, T — Total DOS |h a a M  A A a a-LI I/I 1 .E1 I B:  I a  ■i !)jl-2 0 10 20-10 0 Energy(ev)Figure 4 Density of States (DOS) of the |3-TCP com pound with G G A  calculations.>£roCOW0a6300.80.60.40.20.02.41.81.20.60.00.90.60.30.0A h  /j f l  | ----------T o ta l D O S/ L,= ai[ = si . i tJ \  JL / f l -  sL -------------------- r ^ - t1 = 1|-------------------- t— --------------------20 -10 0 10 20 Energy (eV)Figure 5 Density of States (DOS) of the |3-TCP com pound with m BJ-GGA calculations.3.2 O ptical PropertiesOptical properties and band g a p  calculations provide more information about the analysis and designing materials. Therefore, we performed the optical properties calculations for (3-TCP com pound to get the optical parameters such as, static dielectric constant £i(0), static refractive index n(0), magnitude of the coefficient of reflectivity at zero frequency R(0), number of effective electrons (Neff) for e ach  formula unit and plasmon energy hwp (eV), and the results are shown in Table 1.Table 1 Calcu lated static dielectric constant £i(0), static refractive index n(0), m agnitude of the coefficient of reflectivity at zero frequency R(0), number of effective electrons (Neff) for e a ch  formula unit |3-TCP and plasmon energy hwp.Parameter LDA GGA mBJ-GGA£i(0) 3.3567 3.2368 2.4622£2(0) 0.0000 0.0000 0.0000n(0) 1.8321 1.7991 1.5691R(0) 0.0863 0.0815 0.0490Neff 47.1050 46.645 42.872hwp 8.1250 8.7354 6.9142163 A. M. A. Bakheet et al. / Jurnal Teknologi (Sciences & Engineering) 78: 3-2 (2016) 159-164Table 2: Maximum attained values of refractive index nmax, reflectivity Rmax, optical conductivity amax, absorptivity amax with corresponding energies for the |3-TCP compound.Value at Parameter X C  0GPaEnergy (eV)nmaxLDA 2.419226.13617G G A 2.378036.27223m BJ-GGA 2.05588.55798DRmaxLDA 0.56881228.20461G G A 0.59320228.53115m BJ-GGA 0.70805229.91893amaxLDA 9995.6326.16376G G A 10812.326.54472m BJ-GGA 15691.528.1774^maxLDA 9995.6326.16376G G A10758.926.5175m BJ-GGA 15691.528.1774The maximum values of the refractive index nmax, reflectivity Rmax, optical conductivity amax, absorptivity amax for P-TCP com pound with the corresponding energies are calculated, and the results are presented in Table 2. The obtained values of ca lculated refractive index, reflectivity, optical conductivity, and absorptivity using m BJ-GGA approximation are more accurate  com pared to the obtained ones from LDA and G G A  approximations.4.0 CONCLUSIONDensity functional theory calculations are carried out using (FPL-APW) method along with three types of exchange-correlation potentials, LDA, G G A , and mBJ- G G A. The com puted band g a p  values are 5.2 eV, 5.9 eV and 6.8 eV based on LDA, G G A , and m BJ-G G A techniques, respectively. The band g a p  results show that, P-TCP has direct band g a p  nature. The density of state calculation shows that the upper va lence band energy is between -5eV and -6eV from mixture C aS and C a P  states, but produced additional TDOS structure at -7.5eV in p>-TCP com pound. TDOS and PDOS calculation reveals a number of electronic density of states for m BJ-GGA technique com pared to LDA and G G A . The optical parameter, static dielectric constant £1(0) reaches the values of 3.23681 (eV) at 0G Pa for the p>-TCP com pound. The present results with m BJ-GGA approximation for the exchange  correlation potential present very good agreements with the other theoretical and experimental findings. These investigations provide information about the electronic and optical properties of (3-TCP com pound, which can  be used to fabricate useful and com patible (3-TCP biomaterial for clinical applications.AcknowledgementThe authors would like to thank for the financial support (Foreign A cad e m ic Visitor Grant) of Universiti Teknologi Malaysia (UTM) Skudai, Johor, Malaysia for the grant No.QJ130000.2526.02H93 and Ministry of Higher Education Malaysia for this research work.References[1] S. Quillard, M. Paris, P. Deniard, R. Gildenhaar, G. Berger, L. Obadia, J.-M. Bouler, 2011. 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Theoretical investigations of β-tricalcium

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Theoretical investigations of β-tricalcium

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