Solids Modeled by ab Initio Crystal-Field Methods. 12. Structure, Orientation, and Position of A-Type Carbonate in a Hydroxyapatite Lattice

An approach to investigate the crystallographic unit cell of human tooth enamel

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hydroxyapatite [HAP, Ca10(PO4)6(OH)2] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P63/m or another space group. The observance in HTE of Ca2+, Mg2+ and Na+ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca2+ can be replaced by Na+ and Mg2+ ions; the PO43- group can be replaced by CO32- ions; and the OH- ions can also be replaced by CO32-. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH-, CO32-, Mg2+ and Na+ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg2+, carbonate and interstitial Na+. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

The Mutual Incorporation of Mg2+ and CO32- into Hydroxyapatite: A DFT Study

Hydroxyapatite (HA) with a stoichiometry composition of Ca₁₀(PO₄)₆(OH)₂ is widely applied for various biomedical issues, first of all for bone defect substitution, as a catalyst, and as an adsorbent for soil and water purification. The incorporation of foreign ions changes the acid-base relation, microstructure, porosity, and other properties of the HA materials. Here, we report the results of calculations of the density functional theory and analyze the possibility of two foreign ions, CO₃^2- and Mg²⁺, to be co-localized in the HA structure. The Na⁺ was taken into account for charge balance preservation. The analysis revealed the favorable incorporation of CO₃^2- and Mg²⁺ as a complex when they interact with each other. The energy gain over the sole ion incorporation was pronounced when CO₃^2- occupied the A position and Mg²⁺ was in the Ca(2) position and amounted to -0.31 eV. In the most energy-favorable complex, the distance between Mg²⁺ and the O atom of carbonate ion decreased compared to Mg…O distances to the surrounding phosphate or hydroxide ions, and amounted to 1.98 Å. The theoretical calculations agree well with the experimental data reported earlier. Understating the structure-properties relationship in HA materials varying in terms of composition, stoichiometry, and morphology paves the way to rational designs of efficient bio-based catalytic systems.

Hydroxylapatite and Related Minerals in Bone and Dental Tissues: Structural, Spectroscopic and Mechanical Properties from a Computational Perspective

Hard tissues (e.g., bone, enamel, dentin) in vertebrates perform various and different functions, from sustaining the body to haematopoiesis. Such complex and hierarchal tissue is actually a material composite whose static and dynamic properties are controlled by the subtle physical and chemical interplay between its components, collagen (main organic part) and hydroxylapatite-like mineral. The knowledge needed to fully understand the properties of bony and dental tissues and to develop specific applicative biomaterials (e.g., fillers, prosthetics, scaffolds, implants, etc.) resides mostly at the atomic scale. Among the different methods to obtains such detailed information, atomistic computer simulations (in silico) have proven to be both corroborative and predictive tools in this subject. The authors have intensively worked on quantum mechanical simulations of bioapatite and the present work reports a detailed review addressed to the crystal-chemical, physical, spectroscopic, mechanical, and surface properties of the mineral phase of bone and dental tissues. The reviewed studies were conducted at different length and time scales, trying to understand the features of hydroxylapatite and biological apatite models alone and/or in interaction with simplified collagen-like models. The reported review shows the capability of the computational approach in dealing with complex biological physicochemical systems, providing accurate results that increase the overall knowledge of hard tissue science.

The effect of chemical potential on the thermodynamic stability of carbonate ions in hydroxyapatite

First-principles calculations were performed for CO3(2-) ions in hydroxyapatite in order to investigate the atomic structures and thermodynamic stability of CO3(2-) and its related defects. Two different chemical equilibrium conditions in high-temperature and aqueous-solution environments were considered, and atomic and ionic chemical potentials for the individual chemical equilibrium conditions were evaluated to calculate defect formation energies. It was found that A-type CO3(2-) (substituting OH(-)) is energetically more favorable than B-type CO3(2-) (substituting PO4(3-)) in the high-temperature environment, whereas B-type is preferred to A-type in the aqueous solution environment. This result successfully reproduces experimentally observed trends. In the formation of A-type and B-type CO3(2-), OH(-) vacancies or protons (interstitial or substitutional) act as charge-compensating defects.

Infrared spectroscopic characterization of carbonated apatite: a combined experimental and computational study

A combined experimental and computational approach was employed to investigate the feasibility and effectiveness of characterizing carbonated apatite (CAp) by infrared (IR) spectroscopy. First, an experimental comparative study was conducted to identify characteristic IR vibrational bands of carbonate substitution in the apatite lattice. The IR spectra of pure hydroxyapatite (HA), carbonate adsorbed on the HA surface, a physical mixture of HA and sodium carbonate monohydrate, a physical mixture of HA and calcite, synthetic CAps prepared using three methods (precipitation method, hydrothermal route, and solid-gas reaction at high temperature) and biological apatites (human enamel, human cortical bone, and two animal bones) were compared. Then, the IR vibrational bands of carbonate in CAp were calculated with density functional theory. The experimental study identified characteristic IR bands of carbonate that cannot be generated from surface adsorption or physical mixtures and the results show that the bands at ∼880, 1413, and 1450 cm(-1) should not be used as characteristic bands of CAp since they could result from carbonate adsorbed on the apatite crystals surface or present as a separate phase. The combined experimental and computational study reveals that the carbonate v3 bands at ∼1546 and 1465 cm(-1) are, respectively, the IR signature bands for type A CAp and type B CAp.

First principles NMR study of fluorapatite under pressure

NMR is the technique of election to probe the local properties of materials. Herein we present the results of density functional theory (DFT) ab initio calculations of the NMR parameters for fluorapatite (FAp), a calcium orthophosphate mineral belonging to the apatite family, by using the GIPAW method (Pickard and Mauri, 2001). Understanding the local effects of pressure on apatites is particularly relevant because of their important role in many solid state and biomedical applications. Apatites are open structures, which can undergo complex anisotropic deformations, and the response of NMR can elucidate the microscopic changes induced by an applied pressure. The computed NMR parameters proved to be in good agreement with the available experimental data. The structural evaluation of the material behavior under hydrostatic pressure (from -5 to +100 kbar) indicated a shrinkage of the diameter of the apatitic channel, and a strong correlation between NMR shielding and pressure, proving the sensitivity of this technique to even small changes in the chemical environment around the nuclei. This theoretical approach allows the exploration of all the different nuclei composing the material, thus providing a very useful guidance in the interpretation of experimental results, particularly valuable for the more challenging nuclei such as (43)Ca and (17)O.

Density functional calculations of the properties of silicon-substituted hydroxyapatite

Ab initio density functional plane-wave calculations are performed on silicon-substituted hydroxyapatite (SiHA). Formation energies are obtained for the substitution of a phosphorus atom by a silicon atom in each of the six phosphate groups of the unit cell in turn. It is found that the co-removal of a hydroxyl group to maintain charge neutrality is energetically favourable and the calculated unit cell volumes for the single silicon substitutions agree extremely well with experimental observation. The substitution of a second silicon atom in the unit cell is found to be almost as energetically favourable as the first (and on one site more favourable) and there can be an attractive interaction between the two Si substituents when they are closely separated. However, experimental observation suggests that for this concentration of silicon a phase transformation to a different structure occurs which, because of the imposed boundary conditions, could not be accessed in the calculations. The density of states of the SiHA indicates that new states are introduced deep into the valence band and the band gap decreases by 1.6 eV compared to phase-pure HA. No new states are introduced into the band gap indicating that the Si incorporation does not make the material inherently electrically active. Furthermore a population analysis shows that the Si impurity has only a small effect on the neighbouring ionic charge.

A computational investigation of stoichiometric and calcium-deficient oxy- and hydroxy-apatites

Computer modelling techniques have been employed to qualitatively and quantitatively investigate the dehydration of hydroxyapatite to oxyapatite and the defect chemistry of calcium-deficient hydroxyapatite, where a number of vacancy formation reactions are considered. The dehydration of hydroxyapatite into oxyhydroxyapatite is calculated to be endothermic by E = +83.2 kJ mol(-1) in agreement with experiment, where thermal treatment is necessary to drive this process. Calcium vacancies are preferentially charge-compensated by carbonate ions substituting for phosphate groups (E = -5.3 kJ mol(-1)), whereas charge-compensating reactions involving PO4 vacancies are highly endothermic (E > or =652 kJ mol(-1)). The exothermicity of the charge compensation of a Ca vacancy accompanied by a PO4/CO3 substitution agrees with their co-occurrence in natural bone tissue and tooth enamel. Our calculations of a range of defect structures predict (i) that calcium vacancies as well as substitutional sodium and potassium ions would occur together with carbonate impurities at phosphate sites, but that other charge compensations by replacement of the phosphate groups are unfavourable, and (ii) that the hydroxy ions in the channel are easily replaced by carbonate groups, but that the formation of water or oxygen defects in the channels is thermodynamically unfavourable. Calculated elastic constants are reported for the defect structures.

Coupled substitution of type A and B carbonate in sodium-bearing apatite

A suite of Na-bearing type A-B carbonate hydroxyapatites {Ca(10-y)Na(y)[(PO4)(6-y)(CO3)y][(OH)(2-2x)(CO3)x], x approximately = y} has been synthesized at 1200 degrees C and 0.5-1.0 GPa, and investigated by single-crystal X-ray structure and FTIR spectroscopy. Crystal data for the maximum content of carbonate (11.1 wt%) are a = 9.3855(7), c = 6.9142(4) A, space group P6(3)/m, R = 0.023, R(w) = 0.014. Structural accommodation of the substitutions requires local coupling of Na and channel (type A) and phosphate (type B) carbonate ion defects. The type B carbonate ion is located on the sloping faces of the substituted phosphate group, but is inclined at an angle of 53 degrees to the mirror plane. FTIR spectra have minimal nu3 absorption beyond 1500 cm(-1) and dominant nu2 absorption at 873 cm(-1). Synthetic Na-bearing type A-B apatites (with a high content of type A carbonate) are thus similar in both chemical composition and infrared spectra to biological apatites. The latter are reinterpreted as Na-bearing type A-B carbonate apatites with channel carbonate up to 50% of total carbonate.

A computer modelling study of the uptake, structure and distribution of carbonate defects in hydroxy-apatite

Computer modelling techniques have been employed to qualitatively and quantitatively investigate the uptake and distribution of carbonate groups in the hydroxyapatite lattice. Two substitutional defects are considered: the type-A defect, where the carbonate group is located in the hydroxy channel, and the type-B defect, where the carbonate group is located at the position of a phosphate group. A combined type A-B defect is also considered and different charge compensations have been taken into account. The lowest energy configuration of the A-type carbonate has the O-C-O axis aligned with the channel in the c-direction of the apatite lattice and the third oxygen atom lying in the a/b plane. The orientation of the carbonate of the B-type defect is strongly affected by the composition of the apatite material, varying from a position (almost) flat in the a/b plane to being orientated with its plane in the b/c plane. However, Ca-O interactions are always maximised and charge compensating ions are located near the carbonate ion. When we make a direct comparison of the energies per substitutional carbonate group, the results of the different defect simulations show that the type-A defect where two hydroxy groups are replaced by one carbonate group is energetically preferred (DeltaH = -404 kJ mol(-1)), followed by the combined A-B defect, where both a phosphate and a hydroxy group are replaced by two carbonate groups (DeltaH = -259 kJ mol(-1)). The type-B defect, where we have replaced a phosphate group by both a carbonate group and another hydroxy group in the same location is energetically neutral (DeltaH = -1 kJ mol(-1)), but when the replacement of the phosphate group by a carbonate is charge compensated by the substitution of a sodium or potassium ion for a calcium ion, the resulting type-B defect is energetically favourable (DeltaH(Na) = -71 kJ mol(-1),DeltaH(K) = -6 kJ mol(-1)) and its formation is also promoted by A-type defects present in the lattice. Our simulations suggest that it is energetically possible for all substitutions to occur, which are calculated as ion-exchange reactions from aqueous solution. Carbonate defects are widely found in biological hydroxy-apatite and our simulations, showing that incorporation of carbonate from solution into the hydroxyapatite lattice is thermodynamically feasible, hence agree with experiment.

Inorganic plasma with physiological CO2/HCO3- buffer

The substitution of tris/HCl buffer by CO(2)/HCO(3)(-) buffer in inorganic plasma was studied. An appropriate gas mixture of CO(2)/N(2) was continuously bubbled in Kokubo's SBF solution prepared without addition of Tris/HCl. This method enables buffering the solution within the 7.3-7.4 pH interval and, at the same time, reaching a HCO(3)(-) concentration between 24 and 27 mmol dm(-3), which are the normal concentrations reported for blood plasma. Mineralisation studies on calcium phosphate ceramics using this solution showed that, in the presence of such hydrogencarbonate concentrations, the formation of a mineralisation layer on the ceramic occurs via a carbonated octacalcium phosphate, that evolves to carbonated hydroxyapatite. The results suggest that mineralisation studies in this new carbonate-containing simulated inorganic plasma mimic biomineralisation more closely than traditional SBF.

Calcium phosphate clusters

The potential energy surfaces associated with [Ca3(PO4)2n clusters are analyzed in detail using ab initio calculations for n ranging from one to four. Considering separated clusters, energy criteria favor the so-called Posner's cluster Ca9(PO4)6, which is the core of the actual structural model of amorphous calcium phosphate. This is rationalized through the existence of a distinct CaO bonding pattern in this cluster. Considering aggregated clusters as a possible model for amorphous calcium phosphate, the aggregation of Ca3(PO4)2 clusters appears as an alternative to Posner's hypothesis.