Design of the electronic structure and properties of calcium apatites via isomorphic modification of the cation sublattice, and prospects of their application Open Access

The extension of the physical properties of the apatites, as well as other compounds, can be largely achieved by isomorphic substitutions. Such compounds have a number of beneficial functional properties. Their mechanical, optical, catalytic, and a number of other characteristics can be effectively controlled by isomorphic substitutions in both cationic and anionic sublattices. Thus, the study of the details of chemical bonds and resulting physical properties of apatite-like compounds is an important task.¹ 

The most well-known member of the apatite family is calcium hydroxyapatite [HAP, Ca₁₀(PO₄)₆(OH)₂]—a biocompatible material that is widely used in bone implants,^2–4 scaffolds,^5,6 as a drug delivery agent,^7–9 in bone tissue engineering,^10,11 orthopedics,^12,13 and other biomedical applications.^14–17 

The apatite lattice remains stable for a very wide range of the non-stoichiometric ratio, which opens up the possibility to control the physical and chemical characteristics of synthesized materials using isomorphic substitutions in the apatite structure. This fact expands the areas of application of apatite-like structures, in particular, to wastewater treatment,^18,19 biodiesel production,^20–22 oxidation of volatile organic compounds,^23,24 hydrogen production,^25,26 catalysts synthesis,^27–30 and even such specific applications as cancer theranostics.^31–34 The stability of the apatite crystal lattice in the wide range of non-stoichiometric ratios determines the ability of a compound to easily carry out the sorption of a number of inorganic and organic compounds, such as proteins and bacteria.^35–38 

The introduction of isomorphic substitutions in the apatite structure can lead to new functional features and pave the way for multifunctional applications such as chemical sensors.^39–46 With the help of isomorphic substitutions, it is also possible to control the bandgap and photoconductivity of such compounds. Additionally, this could address specific issues, such as the removal of toxic ions from the active layer of a perovskite solar cell that contains lead, without compromising its efficiency. This problem has become urgent from the point of view of perovskite-based green energy applications.^47–49 

To fully understand and control the physical and chemical properties of apatite-like structures through isomorphic substitutions, it is necessary to establish the fundamental principles of their structure. This involves understanding how the electronic structure is formed based on factors, such as composition, synthesis conditions, dimensions, and topology of key elements, as well as the relationship between the composition and structure of apatite-like compounds and their electronic structure. In this article, we will focus on the isomorphic substitution of calcium atoms with metal atoms in the apatite structure.

Powders of pure and isomorphically substituted calcium hydroxyapatites were obtained by precipitation.^50,51 This method requires significantly lower annealing temperatures and ensures homogenization at the ionic and molecular level, allowing for the production of materials with a high degree of homogeneity. As starting materials, we chose a solution of calcium nitrate Ca(NO₃)₂ with a molar concentration of 1.08 mol/l, a 25% aqueous ammonia solution NH₃⋅H₂O to adjust the acidity of the reaction medium, and a solution of phosphoric acid H₃PO₄ (with a mass concentration of 85% and density of 1.689 g/ml) as both a source of phosphorus and a precipitant. To prepare the precipitating agent solution, 8.2 ml (13.8 g) of concentrated phosphoric acid H₃PO₄ was poured into a 3000 ml chemical beaker, and approximately 2000 ml of distilled water was added to form a dilute acid solution with a concentration of 7 g/l. After that, it was heated to 70–80 °C. Then, 110 ml of 25% ammonia solution was added until pH reached 9. In the process, the solution was being thoroughly mixed on a magnetic stirrer to establish the concentration equilibrium.

At the same time, 360 ml of distilled water was being added to 184 ml of the initial solution of calcium nitrate in an 800 ml chemical beaker while being stirred. The resulting solution was poured into a funnel with a Teflon stopcock.

The precipitate was filtered using a Büchner funnel and washed with distilled water in the ratio V_(water):V_{(precipitate)} = 10:1. The sample was first air-dried for 48 h and then heat-treated in a muffle furnace at 200 °C for 4 h at a heating rate of 5 °C/min.

To obtain hydroxyapatite powders substituted with metal ions, Mg(NO₃)₂, CuSO₄, Fe(NO₃)₃, and Ni(NO₃)₂ (Sigma-Aldrich, Germany) were used as sources of Mg, Cu, Fe, and Ni, which were added to a solution of calcium nitrate. Different molar amounts were used according to different exchange ratios X_Metal/X_Ca.

The diffractogram for the synthesized stoichiometric hydroxyapatite powder confirmed the single-phase nature of the apatite obtained (see the supplementary material).

The IR spectra of the samples were obtained using a SPECORD M80 double-beam spectrophotometer. The samples were prepared for the measurement by pressing a mixture of the investigated compound and KBr powder into tablets. Transmission spectra were recorded in the absorption range of tetrahedral sublattices (ХО₄)³⁻, the vibrational modes of which lie in the region from 1600 to 400 cm⁻¹. In the region of longer wavelength, the sharp absorption of KBr powder begins; therefore, measurements in the range below 400 cm⁻¹ were not carried out. During the measurements, the sample chamber was blown with dry air to thoroughly dry the samples from water vapor.

The optical absorption spectra of the samples were obtained on a Spekol 1500 spectrophotometer in the wavelength range of 190–1100 nm. The spectral features observed in the range of 450–800 nm can be attributed to interruptions in the scanning process of the samples that were fabricated in the form of a colloidal solution of the investigated compound in distilled water. These interruptions caused the scanner to stop for some time, resulting in the distinct steps observed in the spectra.

The x-ray photoelectron spectra of the core levels of elements of the analyzed compounds were taken on the PERKIN ELMER PHI 5600 x-ray spectrometer, using Al K_α radiation and a monochromatized beam. The beam diameter was set to 400 μm. An electron gun was used to compensate for sample charging. The vacuum level during the experiment was at least 10⁻⁷ Pa. The energy resolution was equal to 0.1 eV. The calibration of binding energies was carried out using the 1s line of carbon of hydrocarbon residuals on the surface of the samples. The resulting energy is 284.0 eV.

We employed the density functional theory (DFT) within the framework of Wien2k package^52,53 to perform quantum mechanical calculations. Specifically, we used the full-potential linearized (α ⋅ hν)^1/γ = B(hν − E_g) augmented plane-wave + local orbitals method [(L)APW + lo] with the Purdue–Burke–Ernzerhoff generalized gradient approximation for solids (PBEsol-GGA).⁵⁴ The k-mesh was set to 2-2-3 according to Martins' method.⁵⁵ We calculated the density of electronic states using the tetrahedron method⁵⁶ with the atomic coordinates obtained through relaxation. We used the full-potential APW method with a set of basis functions (APW + lo + LO) to calculate the electronic structure and total and partial density of states (DOS) while taking into account the relaxation of atomic positions. The orbitals Ca 3s, Ca 3p, and P 2p were considered as valent (LO). Finally, we utilized the generalized gradient approximation (GGA)⁵⁴ method to compute the exchange-correlation potential.

The general regularities of the formation of the valence band of stoichiometric calcium hydroxyapatite—Ca₁₀(PO₄)₆(OH)₂ and the partial contributions of the valence electrons of atoms are described by us in Ref. 1. The presence of the feature G [Fig. 1(a)], the position of which in a pure metal corresponds to the interaction between calcium atoms, confirms the presence of such an interaction in calcium apatite. It should be noted that the minimum distance between calcium atoms is 3.96 Å [Ca₍₁₎—Ca₍₂₎] and it corresponds to the distance between calcium atoms in different crystallographic positions of an apatite. This distance correlates with the position of the external valley of the effective potential for calcium d-electrons.^65,66 It may, therefore, indicate the existence of hybridized valence electron states corresponding to the energy levels of the external valley of the effective potential for calcium d-electrons. The presence of a feature in this region on the O₍₄₎ electron density curve indicates that a possible channel of such interaction is the indirect Ca–O–Ca interaction through O₍₄₎ oxygen atoms.

Hybridized s-, p-, and, in part, d-electronic states of calcium and phosphorus ions make the main contribution to the formation of the main features of the upper part of the valence band. The structure of subvalent states in the region between ∼18 and ∼26 eV is determined by the s-states of oxygen and phosphorus. A comparison of total density of states (DOS) quantum mechanical simulations of [ХО₄]³⁻ ions, where Х = P, V, As, with simulations of apatites showed a remarkable similarity of the total density of states curves and made it possible to conclude that the sublattice of oxygen tetrahedra is decisive in the formation of the shape and main features of the DOS curves of calcium apatites.¹ 

The substitution of the hydroxyl group in calcium hydroxyapatite with fluorine and chlorine atoms is accompanied by an increase in deformation of the PO₄ tetrahedra in the OH⁻ → F⁻ → Cl⁻ series. The half-widths of absorption bands characterizing the [PO₄]³⁻ ion in apatites are 190, 210, and 420 cm⁻¹ for Ca₅(PO₄)₃OH, Ca₅(PO₄)₃F, and Ca₅(PO₄)₃Cl, respectively, with the measurement error of 3 cm⁻¹. At the same time, for the fluorapatite and hydroxyapatite, the crystallographic ratio c/a remains at 0.73, while for the chlorapatite, this parameter is equal to 0.70, and the unit cell volume decreases in the series Ca₅(PO₄)₃Cl, Ca₅(PO₄)₃OH, and Ca₅(PO₄)₃F.¹ 

Curves of total densities of electronic states of calcium fluorapatite atoms compared to hydroxyapatite are characterized by a much larger splitting, which correlates with higher symmetry of hydroxyapatite tetrahedra compared to fluorapatite. A similar trend is observed for strontium hydroxyapatite as compared to fluorapatite.

Heavy metal apatites retain the same tendency to form curves of total densities of electronic states as stoichiometric calcium apatite [Fig. 1(b)]. One of the features of the electronic structure of Pb₁₀(PO₄)₆(OH)₂ is the ability of the inactive electron pair 6s² to participate in the bond. Thus, for the Pb²⁺ state, two 6s-electrons can be described as a lone pair; however, depending on the environment, the unoccupied 6p-orbital may hybridize with the 6s-orbital, which leads to the formation of a “stereochemically active” lone pair. Such an electron pair actively interacts with the О 2p valence electrons of the surrounding oxygen and leads to the participation of the previously inactive electron pair in the lead–oxygen chemical bond. Moreover, for those lead atoms situated in the second crystallographic position, such hybridization turns out to be significantly less pronounced.

Metals from the actinide series, along with heavy metals such as Pb and Sn, are commonly utilized in modern industrial processes. Consequently, research interest has been sparked in the investigation of their accumulation and migration paths.^67–74 Among the actinoids, uranium is one of the most frequently employed elements, and it exists in nature in two valence states, U⁴⁺ and U⁶⁺. Given the close ionic radii of U⁴⁺ (0.93 Å) and Ca²⁺ (0.94 Å), various isomorphic substitutions are possible within the apatite structure. Uranium does not generally act as an isomorphous impurity in natural calcium minerals but forms a mineral phase in the form of micro-inclusions. Nevertheless, it is feasible to synthesize calcium hydroxyapatite isomorphically modified with uranium in a laboratory. Calcium is only included in the composition of uranium minerals as an isomorphous impurity if rare earth elements (REEs) are also present. The specifics of natural and artificial actinoid migration in various systems are considered in our research.^67–70 

A key issue in understanding the electronic structure of actinide-based compounds is the role of 5f-electrons. The question is, if 5f-electrons remain localized, as is the case for 4f-electrons in REEs, or their states have a band character. It was shown in Ref. 75 that the degree of delocalization of 5f-electrons in actinoids is even higher than that of 3d-electrons of elements of the first transition metal period.

The DOS curve of stoichiometric HAP is significantly affected by the isomorphic addition of uranium. This is due to the fact that because of the mismatch of the radii of Ca and U atoms, the introduction of uranium into the HAP lattice results in a decrease in tetrahedra symmetry and leads to splitting, displacement, and the emergence of new peaks on the DOS curve (Fig. 1). The correlation between the shifts of x-ray electron lines and the calculated data suggests that uranium atoms have a tendency to enter the Ca₍₂₎-position in the lattice.

Isomorphic modification of the apatite calcium phosphate matrix with alkali and rare earth metals causes a considerable redistribution of the electron density of the crystal, leading to changes in the shape of the DOS curve characterizing the valence band. In contrast to phosphate apatites, isomorphic substitutions in their vanadate counterparts do not significantly affect the shape of the DOS curve (Fig. 2).

The structure of the DOS curve peaks of Ca₈NaX(VO₄)₆(OH)₂, where X = La, Nd, Sm, Gd, Ho in the series La → Nd → Sm → Gd → Ho, undergoes only slight changes upon isomorphic modification of calcium hydroxyvanadate with sodium and REMs. It only results in a collective shift of all the groups of features toward higher binding energies. The preferred position of the rare earth element in the apatite structure is the Ca₍₂₎-position.

The observed changes in the curves of the partial densities of f-states of Lanthanum in the studied series of compounds Ca₈LaX(VO₄)₆(OH)₂, with X = Li, Na, K, Rb, Cs, can be attributed to interactions in the metal sublattice, which do not have a significant effect on the formation of the shape of the partial DOS curves (Fig. 3). In the sodium-containing compounds Ca₈NaX(VO₄)₆(OH)₂, with X = La, Nd, Sm, Gd, Ho, in the substitution series La → Nd → Sm → Gd → Ho, more significant changes in the curve of REE f-states were observed. In general, for all compounds, except for the samarium compound, the partial f-density curves had the same patterns as the total DOS curves, indicating active participation in the formation of a chemical bond. On the other hand, samarium f-states had a significantly higher relative intensity and were localized around 13.0 eV, indicating a much higher core nature of this level.

In addition, we analyzed the ionic charges in a series of the studied apatites within the framework of DFT using the Wien2k package. The detailed results of the Atoms-in-Molecules (AIM)⁷⁶ analysis of the ionic charges of the compounds Me₁₀(PO₄)₆X₂, where Me = Ca and Cd, and X = F, Cl, Br, are presented in Tables 2 and 3 in the supplementary material. When comparing the charges of Ca₍₁₎ and Ca₍₂₎ ions, we conclude that the charge of Ca₍₁₎ is almost the same (+1.61 e) for all calcium compounds, while the charge of Ca₍₂₎ depends significantly on the type of anion on the c axis. The average charge of phosphorus ions for calcium and cadmium apatites is +3.66 e, and there is no obvious correlation with the electronegativity of the anion located on the c axis. For fluor-, chlor-, and hydroxyapatites of calcium and cadmium, the deviation of the phosphorus ionic charge from the average is small and does not exceed 0.025 e.

The bandgap width of Ca₁₀(PO₄)₆X₂ compounds, where X = F, Cl, OH, is shown in Table I. It can be seen that of all calcium phosphate apatites, calcium fluorapatite has the largest bandgap of 5.9 eV. The calculated value is 5.6 eV, which is 0.3 eV less than the experimental value. This is explained by the peculiarities of quantum mechanical calculations, namely, the calculated gap is defined as $E N + 1 N− E N N$⁠, while the experimental one is defined as $E N + 1 N + 1− E N N$ (where the superscript corresponds to the number of electrons in the system, the subscript corresponds to the band number, and E is the total energy of the band). Thus, the difference between the experimental bandgap and the theoretical one is $E N + 1 N + 1− E N + 1 N$⁠. A similar trend is observed for Ca₁₀(PO₄)₆Сl₂ and Са₁₀(PO₄)₆(ОН)₂. It should be noted that the width of the bandgap depends on the particle size and the method of synthesis of a specimen.

Which exact localized electronic states are responsible for the formation of the bandgap in calcium apatites can be demonstrated clearly, for instance, in calcium chlorapatite. Figure 4 illustrates the distribution of electron densities of the “near-Fermi” region between E(HOMO)-12.0 eV and E(HOMO), as well as the electron density distribution of the unoccupied portion of the valence band between LUMO and LUMO + 13.0 eV in the (001) plane, which passes through the point (0; 0; ¼) in calcium chlorapatite.

The section of the electron density distribution in this plane was chosen considering the fact that it contains all types of atoms, namely, Са₍₂₎, Р, О₍₁₎, О₍₂₎, and Cl atoms, and, therefore, reflects the distribution of electronic densities along most bonds. It can be seen (Fig. 4) that for calcium chlorapatite, the “near-Fermi” region is formed mainly by O 2p- and Cl 3p-states. At the same time, the electron density at calcium atoms in this region is low.

In Ca₁₀(PO₄)₆Cl₂, the electron density of calcium is formed mainly by Ca 3d-states, the density of which rapidly decreases with the distance from the nucleus. Oxygen atoms are shown to have a small number of unoccupied 2s electronic states, which are localized in the immediate vicinity of the nucleus. An anomalous distribution of the electron density in the coordinate space for the unoccupied part of the valence band, which is formed mainly by P 3p-states, was recorded for phosphorus atoms. In the immediate vicinity of the nucleus, the electron density of the unoccupied part of the valence band around the phosphorus atom is insignificant, while it has intensity maxima at some distance from the nucleus along the lines connecting the phosphorus atoms with the centers of the oxygen planes, that is, along the lines that are the most distant from P–O bonds.

The total density of states curves for Са₁₀(PO₄)₆(ОН)₂ in the unoccupied part of the valence band reveal the presence of states that are not observed in Ca₁₀(PO₄)₆F₂. These states are located closer to the HOMO energy than the Ca 3d-states and result from the hybridization of 1s-states of H atoms and 2p-states of O atoms from the hydroxyl group. The narrowing of the energy gap by 0.3 eV upon replacing fluorine ions with hydroxyl groups in Ca₁₀(PO₄)₆F₂ is due to the appearance of these states.

The optical absorption spectra of the phosphate apatites that underwent isomorphic substitutions in the cationic sublattice are shown in Fig. 5. The absorption peak at ∼340 nm is observed. When Ca is partially replaced by Mg or Fe in hydroxyapatite, the appearance of additional features in the near-infrared range is observed [Fig. 5(a)]. At the same time, the peak at ∼340 nm corresponds to the O²⁻ → P⁵⁺ transition in the PO₄³⁻ sublattice.⁷⁷ The characteristic peak near 205–220 nm region reflects transitions during O²⁻ → Ca²⁺ charge transfer.^78,79 It is believed⁸⁰ that the absorption in the visible range is caused by the formation of oxygen vacancies. This phenomenon is called coring^81,82 and is most likely caused by a decrease in the ionic charge of metal atoms inside the sample. When hydroxyapatite is exposed to UV radiation, it results in the formation of an oxygen vacancy in its lattice and an electron in the valence band. The electron then combines with atmospheric oxygen to create an oxygen free radical. This effect highlights the potential use of hydroxyapatite in the field of photocatalysis.⁸³ 

Stoichiometric calcium apatite samples, and those doped with Fe and Mg, show a nearly constant reflectance ratio within the 400–1100 nm range.

The bandgap width calculated from the absorption spectra for the pure apatite has a value of 5.2 eV [Fig. 5(b)], which coincides with the data obtained by other methods: the range of the bandgap values is 4.9–5.6 eV.^58,77,84,85 A narrowing of the energy gap is observed for samples that experienced isomorphic substitutions in the cation sublattice (Table II). The most significant narrowing is observed upon substitution with nickel and copper: 3.2 and 3.4 eV, respectively. The isomorphic substitution of calcium in the apatite structure by atoms of 3d-metals leads to the appearance of 3d electronic states in the crystalline bandgap, which causes a change in its width. With such substitutions, a change in the color of the sample can be observed due to the appearance of color centers. Such effects are often observed in studies of apatites of biogenic origin. Thus, the color of human bone mineral has a significant dependence on age. The color of the bone of an elderly person has an orange tint due to the accumulation of various metals in the bone mineral.

Overall, the isomorphic modification of calcium apatite by atoms of 3d-metals shows a general tendency to decrease the bandgap width with an increase in the serial number of the 3d-metal.

The electronegativity is a fundamental chemical property of an atom. It is a quantitative characteristic representing the ability of an atom in a substance to attract electrons of other atoms. The highest degree of electronegativity is found in halogens and strong oxidizers, while the active metals, such as Na, K, and Cs, have the lowest. A comparison of the electronegativity of Mg (1.54), Ca (1.15), Fe (1.72), Co (1.83), Ni (1.92), and Cu (2.30) shows its increase as the ordinal number of the 3d-metal increases. Since the electronegativity of calcium has a smaller value than that of 3d-metals, then upon introduction of isomorphic substitutions, the greatest effect on the structure should be expected for substitutions by elements with the highest electronegativity. This is what we attempted to clarify using the infrared spectroscopy method.

The effect of isomorphic substitution on the oxygen sublattice can be observed in infrared spectra. The IR spectrum of calcium hydroxyapatite¹ is characterized by two intense groups of bands near 1040 and 570 cm⁻¹. As is known,⁸⁶ there exist nine possible vibrations of the ХО₄ group. If all Х–О bonds are equivalent, i.e., in the case of tetrahedral symmetry T_d, they result in just two bands in the IR spectrum: v₃ and v₄ vibrational bands. In the case when all four bonds are different (C_s symmetry), the lifting of the doubly degenerate v₂ oscillation appears. It can be seen from Table II that the width of the lines corresponding to the vibrations of the PO₄ group with isomorphic substitutions increase significantly. This indicates a decrease in the symmetry of the (PO₄)³⁻ anion in the apatite sublattice, as compared to stoichiometric calcium apatite. Moreover, for apatites doped with nickel and copper, for which the most notable bandgap narrowing was found, a larger broadening of the PO₄ absorption bands of tetrahedra is observed, i.e., a decrease in the symmetry of tetrahedra (Table II).

In order to study the effects associated with the change in the charge states of atoms upon doping and to assess the state of the oxygen–metal bond, x-ray photoelectron spectra of the O 1s of investigated compounds were obtained (Fig. 6). According to the study,⁸⁷ the interatomic interaction between calcium atoms and dopants in the apatite is carried out indirectly through the oxygen matrix and is realized with the participation of oxygen s- and p-electrons following the scheme Ca(Me)–O–Ca(Me) for calcium/substitute and P–O–P for phosphorus, respectively. Therefore, the O s x-ray photoelectron spectra contain components that correspond to these interactions. By examining the decomposed components of the provided О 1s spectra (Fig. 6), we can observe the presence of oxygen in three distinct states, which indicate the interaction between the oxygen matrix and the metal (Me–O), phosphorus (P–O) located in the center of the tetrahedra, and the O–H bond.⁸⁴ For stoichiometric calcium hydroxyapatite, these components are found at ∼530.5, ∼531.5, and ∼532.5 eV, respectively.^88,89 Such discrepancies between the corresponding energy bonds allow for an accurate decomposition into the components of the oxygen spectra. It can be seen that the isomorphic substitution of calcium by iron leads to a decrease in the percentage of the metal–oxygen bond and a slight redistribution between other components. If the contribution of the component responsible for the O–H bond remained unchanged, then it could be argued that the isomorphic replacement of calcium atoms by iron atoms occurs exclusively in the first crystallographic position –Са₍₁₎, due to the fact that the calcium atom in this position has an environment that consists exclusively of tetrahedra of oxygen atoms. However, as this component undergoes a notable shift in its contribution to the overall chemical bond balance, it can be concluded that iron atoms primarily enter the apatite structure at the Ca₍₂₎-position, where the triangle of metal atoms is centered by the hydroxyl group. When calcium atoms are replaced by iron atoms in the structure of calcium apatite, an increase in the binding energy of all components of the O 1s decomposition is observed, with a simultaneous increase in the energy of the center of mass of the spectrum, which indicates a decrease in the electron density at the locations of oxygen atoms in case of such isomorphic substitution.

In general, the replacement of calcium atoms by atoms of 3d-metals in the apatite structure leads to an average three percent decrease in the contribution of the Me–O component to the overall chemical bond of oxygen atoms. The increase in the component associated with the O–H bond can indicate an enhancement in the Me₍₂₎–O bond along the c axis within the triangle of metal atoms. When calcium atoms are replaced with magnesium atoms, the opposite effect is observed. The component representing the Me–O bond increases by several percent compared to the stoichiometric sample. This phenomenon is likely due to the fact that magnesium, being in the same group of elements as calcium, has a slightly different radius. As a result, despite the same charge compensation ability, it has a different electron affinity energy, leading to an observable increase in the oxygen–metal bond.

Isomorphic substitution of calcium ions by heavy metal ions in the cationic sublattice of calcium hydroxyapatite changes the shape of the energy curve of the occupied part of the valence band only slightly. It retains a pronounced band character with different lengths of individual subbands, namely, the upper and the lower parts of the valence band. It was established that the most probable point of entry of REEs and uranium atoms into the apatite lattice is the Ca₍₂₎-position. It opens up the prospect of creating structures for the long-term disposal of radioactive waste and other toxicants based on heavy metals.

f-states of rare earth elements in the isomorphically substituted compounds Ca₈NaX(VO₄)₆(OH)₂, with X = La, Nd, Sm, Gd, Ho, demonstrate a significant core-like behavior, with the exception of the samarium-containing compound for which an increase in the f-state contribution to DOS is observed, as compared to La, Nd, Gd, and Ho-containing compounds. This can be attributed to the fact that among all the REMs that were investigated, only samarium can exhibit both +2 and +3 valency.

With the increase in the ordinal number of both the alkali metal and the REM upon isomorphous substitution, a decrease in the total energy of the apatite crystal is observed, which is in line with the challenges in obtaining impurity-free apatite single crystals, and the lack of stoichiometric apatite single crystals found naturally. Small deviations of the total energy per unit cell during the transition from Ca₁₀(PO₄)₆Сl₂ to Ca₁₀(PO₄)₆F₂ indicate the high lability of the anion along the c axis.

The average charge of calcium ions in Са₁₀(PO₄)₆X₂ compounds, where X = F, Cl, ОН, amounts to +1.61 of the electron charge, and changes little when the type of an anion located on the sixth order axis changes. When the anion on c axis is substituted, the electronic charge of calcium atoms in the first and second non-equivalent positions is redistributed. Specifically, a reduction in the electronegativity of the anion along the sixth order axis leads to an increase in the charge of the Me₍₁₎ ion and a decrease in the charge of the Me₍₂₎ ion.

Isomorphic substitution of calcium atoms by metal atoms (Fe, Ni, Cu, Mg) in the apatite structure in the range of 1%–2% of atomic concentration leads to the narrowing of the energy gap. The most substantial narrowing is observed when calcium is substituted with nickel and copper. Substitution of calcium atoms by atoms of 3d-metals in the calcium apatite structure only leads to a small decrease in the Me–O interaction compared to the stoichiometric sample.

The ionic charge of oxygen for various nonequivalent positions in the Ca₁₀(PO₄)₆X₂ series, where X = F, Cl, Br, OH, undergoes significant changes, with O₍₂₎ exhibiting the largest ionic charge, and O₍₃₎ exhibiting the smallest for the investigated calcium apatites. The average charge of the phosphorus ion for these compounds is approximately +3.66 of the electron charge, suggesting a significant electron charge outflow from phosphorus atoms to oxygen atoms.

The theoretically calculated bandgap of calcium apatites is accurately described in terms of the generalized gradient approximation. The ability to control the bandgap of calcium apatites by isomorphic substitutions opens up new possibilities for their practical application, for instance, as components of solar cells based on perovskites.

See the supplementary material for the detailed x-ray diffraction data for Ca-HAP powder samples, and the tables of ionic charges obtained by AIM analysis for the compounds Me₁₀(PO₄)₆X₂, where Me = Ca and Cd, X = OH, F, Cl, Br.

We acknowledge financial support from the Ukraine Scientific Scholarship Program Dresden (UKRAPRO) and the National Academy of Sciences of Ukraine (Project No. 6.8/23-P).

The authors have no conflicts to disclose.

V. Karbivskyy: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). N. Kurgan: Data curation (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (lead); Writing – review & editing (equal). M. Hantusch: Data curation (equal); Methodology (supporting); Writing – review & editing (supporting). A. Romansky: Data curation (equal); Investigation (equal); Software (lead); Writing – review & editing (equal). I. Sukhenko: Methodology (supporting); Software (supporting); Writing – review & editing (supporting). L. Karbivska: Investigation (supporting); Methodology (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.