First-Principle Study of Electronic Structure and Atomic Architecture of Vanadate Apatites of Calcium and Cadmium
DOI:
https://doi.org/10.31649/1997-9266-2024-177-6-161-171Keywords:
density functional theory, apatite, electronic structure, Bader analysis, atomic structureAbstract
The electronic structure of the apatite series Me10(VO4)6X2, where Me represents calcium (Ca) or cadmium (Cd) and X denotes fluoride (F), chloride (Cl), or hydroxide (OH), was computed through first principles within the framework of electron density functional theory (DFT). This calculation utilized the full-potential all-electron APW method, supplemented by a set of basis functions (APW + lo). The generalized gradient approximation (GGA) was employed for the exchange-correlation component of the potential, specifically the PBE (Perdew, Burke, Ernzerhof) functional, which is widely recognized in GGA applications. To achieve convergence in the computational results, we examined the dependency on k-grids during structural relaxation, ultimately determining that a 2–2–3 Monkhorst-Pack k-grid centered at the Γ point yields optimal results. The atomic position relaxation for the compounds Me10(VO4)6X2 (Me = Ca or Cd; X = F, Cl, OH) was conducted within the space group P63/m. For the specific compounds Ca10(VO4)6(OH)2 and Cd10(VO4)6(OH)2, we employed the P63 group. The reduction in symmetry observed in hydroxyapatites, in contrast to chloro- and fluoroapatites, is attributed to the incorporation of two additional hydrogen atoms along the c-axis. This alteration results in a symmetry violation concerning the mirror planes that are perpendicular to the axis intersecting the points (0, 0, 0.25) and (0, 0, 0.75).
Bader analysis was performed to elucidate the nature of the chemical bonding. We assessed the evolution of the electronic energy structure within the valence and forbidden bands for the aforementioned apatite series. Additionally, we calculated the parameters associated with the unit cells of these apatites. Our findings indicate that the "near-Fermi" region of the total densities of states is predominantly influenced by the electronic states of oxygen (2p) and cadmium (4d) states within the cadmium apatites. The subvalence states are primarily derived from the 2s states of oxygen. The electronic 3d states of vanadium exhibit a minimal contribution to the "near-Fermi" region, while the bottom of the conduction band is chiefly formed by the calcium (3d) and vanadium (3d) states. Furthermore, we established that the V―O bond is primarily dictated by a strong interaction between O 2p and V 3d states.
Notably, as the electronegativity of the anion X (F, Cl, OH) decreases, the gap width exhibits a slight reduction of a few tenths of an electron volt. On the other hand, substituting calcium with cadmium leads to a significant decrease in the gap width of approximately 0.6 electron volts.
Thus, density functional theory (DFT) with exchange-correlation potential PBE makes it possible to accurately calculate the lattice parameters for calcium and cadmium apatites and the band gap widths for calcium apatites. However, a significant reduction in the gap width when calcium atoms are replaced for cadmium still requires experimental confirmation.
References
L. I. Karbivska, and V. L. Karbivskii. Apatites and tetraoxide compounds, Kyiv: Akademperiodyka, “Ukrainian scientific book in a foreign language“, 2019, 232 p.
T. Kanazawa, Inorganic “Phosphate Materials. Materials Science Monographs,” Elsevier Science, London, 1989.
J. C. Elliot, “Structure and Chemistry of the Apatites and Other Calcium Orthophosphates,” Studies in Inorganic Chemistry, Amsterdam: Elsevier, 1994.
F. Fernane, et al., Materials Characterization, 59: 554, 2008.
A. Yasukawa, et al., “Colloids and Surfaces A: Physicochem,” Eng. Aspects, 299: 203, 2007.
K. Sato, Y. Suetsugu, and J. Tanaka, Journal of Colloid and Interface Science, 224, no. 1: 23, 2000.
J. Y. Kim, R. R. Fenton, B. A. Hunter et al., Australian Journal of Chemistry, 53, no. 8: 679, 2000.
P. A. Henning, M. Moustiakimov, and S. Lidin, Journal of Solid State Chemistry, 150, no. 1: 154, 2000.
M. Greenblatt, and J. H. Pifer, Journal of Chemical Physics, 66, no. 2: 559, 1997.
D. Haverty, Tofail SAM, K. T. Stanton, and J. B. McMonagle, “Structure and stability of hydroxyapatite: density functional calculation and Rietveld analysis,” Physical Review B 71(9), 094103, 2005.
C. X. Li, Y. H. Duan, and W. C. Hu, “Electronic structure, elastic anisotropy, thermal conductivity and optical properties of calcium apatite Ca5(PO4)3X (X = F, C or Br),” Journal Alloy Compd. 619, 66, 2015. https://doi.org/10.1016/j.jallcom.2014.09.022 .
P. Rulis, H. Yao, L. Ouyang, and W. Y. Ching, “Electronic structure, bonding, charge distribution, and X-ray absorption spectra of the (001) surfaces of fluorapatite and hydroxyapatite from first principles,” Physical Review B, 76(24):245410, 2007. https://doi.org/10.1103/PhysRevB.76.245410 .
T. Tamm, and M. Peld, “Computational study of cation substitutions in apatites,” Journal Solid State Chem., 179, 5, 1581, 2006. https://doi.org/10.1016/j.jssc.2006.02.012 .
L. Calderín, M. J. Stott, and A. Rubio, “Electronic and crystallographic structure of apatites,” Physical Review B, 67(13), 134106, 2003. https://doi.org/10.1103/PhysRevB67.134106 .
P. Rulis, L. Ouyang, and W. Y. Ching, “Electronic structure and bonding in calcium apatite crystals: hydroxyapatite, fluorapatite, chlorapatite, and bromapatite,” Physical Review B, no. 70 (15):155104, 2004 .
R. Astala, L. Calderin, X. Yin, and M. J. Stott, “Ab initio simulation of Si-doped hydroxyapatite,” Chemistry of Materials, no. 18 (2), 413, 2006.
V. S. Bystrov, et al. “Computational study of the hydroxyapatite structures, properties and defects,” Journal of Physics D Applied Physics, no. 48, pp. 195302, 2015. https://doi.org/10.1088/0022-3727/48/19/195302 .
Igor V. Pekov, et al. “Pliniusite, Ca5(VO4)3F, a new apatite-group mineral and the novel natural ternary solid-solution system pliniusite–svabite–fluorapatite,” American Mineralogist, no. 107 (8), pp. 1626-1634, 2022.
M. Matsuura, and H. Okudera, “Structures of Ca5(VO4)3Cl and Ca4.78(1)Na0.22(PO4)3Cl0.78: Positions of channel anions and repulsion on the anion in apatite-type compounds,” Acta Crystallographica Section B, no. 78 (5), pp. 789-797, 2022. https://doi.org/10.1107/S2052520622008095 .
H. Song; J. Liu, and H. Cheng, “Structural and spectroscopic study of arsenate and vanadate incorporation into apatite group: Implications for semi-quantitative estimation of as and V contents in apatite,” Spectrochim Acta a Mol Biomol Spectrosc. 188:488494, 2018. https://doi.org/10.1016/j.saa.2017.07.028 .
S. K. Gupta, P. V. R. Rao, and T. S. B. Narasaraju, “Physico-chemical aspects of calcium vanadate apatite,” Journal of Materials Science, no. 21, pp. 161-164, 1986. https://doi.org/10.1007/BF01144715 .
Carlos Bauer Boechat, Jean-Guillaume Eon, Alexandre Malta Rossi, Carlos André de Castro Perezd and Rosane Aguiar da Silva San Gile, “Chemical Physics Structure of vanadate in calcium phosphate and vanadate apatite solid solutions,” Physical Chemistry, issue 18, 2000.
P. Blaha, K. Schwarz, F. Tran, R. Laskowski, G. K. H. Madsen and L. D. Marks, “WIEN2k: An APW+lo program for calculating the properties of solids,” Journal of Chemical Physics, no. 152, 074101, 2020.
J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Lett., no. 77, issue 18: 3865, 1996.
H. J. Monkhorst, and J. D. Pack, “Special Points for Brillouin-Zone Integrations,” Physical Review B, 13: 5188, 1976.
G. Matteo, et. al., “Understanding correlations in vanadium dioxides from first principles,” Physical Review Lett., no. 99, pp. 266402-1-266402-4, 1996.
A. P. Soroka, V. L. Karbovskiy, V. H. Kasianenko, “First-principles study of electronic, atomic structures, phonon spectra and dielectric properties of calcium and cadmium apatites,” Functional Materials, no. 22 (1), pp. 79-92, 2015. http://dx.doi.org/10.15407/fm22.01.079 .
B. Amadon, F. Jollet, and M. Torrent, “γ and β cerium: LDA+U calculations of ground-state parameters,” Physical Review B, no. 77, 155104, 2008. https://doi.org/10.1103/physrevb.77.155104 .
G. Henkelman, A. Arnaldsson, and H. Jónsson, “A fast and robust algorithm for Bader decomposition of charge density,” Computational Materials Science, no. 36, pp. 354-360, 2006.
M. Yu, and D. R. Trinkle, “Accurate and efficient algorithm for Bader charge integration,” Journal of Chemical Physics, no. 134, 064111, 2011.
P. Wu, Y. Z. Zeng, and C. M. Wang, “Prediction of apatite lattice constants from their constituent elemental radii and artificial intelligence methods,” Biomaterials, vol. 25, issue 6, pp. 1123-1130, 2004. ISSN 0142-9612. https://doi.org/10.1016/S0142-9612(03)00617-3 .
Downloads
-
pdf (Українська)
Downloads: 0
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
