Structural, Optoelectronic, and Mechanical Tuning of Ytterbium-Doped Hydroxyapatite: A Combined Experimental and DFT+U Investigation

1. Introduction

Hydroxyapatite (HAp) is widely recognized as the principal inorganic constituent of human bones and teeth, making it a premier material for dental implants and tissue engineering due to its exceptional biocompatibility and osteoconductivity [1,2]. Despite these advantages, pure HAp exhibits inherent limitations, including insufficient mechanical strength, a lack of radiopacity, and limited functional versatility [1,2]. These shortcomings restrict its full potential in advanced odontological procedures, motivating the exploration of ionic doping to tailor and enhance its properties [1].

Among various dopants, rare-earth elements such as ytterbium (Yb) have attracted significant interest for biomedical applications [2,3]. The substitution of calcium (Ca) ions by Yb in the HAp lattice can introduces new electronic states and modify the band structure, leading to distinctive photoluminescent properties and enhanced radiopacity [2,4,5]. These optoelectronic improvements are particularly promising for biomedical imaging, implant tracking, and multifunctional diagnostic platforms [2,4,5]. Furthermore, controlled Yb doping may improve mechanical properties, including microhardness and fracture toughness, while preserving the material’s biocompatibility, making Yb doped HAp highly attractive for minimally invasive dental applications [6,7].

While the synergistic effects of rare-earth co-doping such as Yb combined with Er, Tm, or Zn, have been extensively investigated to enhance luminescence and bioactivity [8,9,10], the fundamental potential and structural dynamics of single-Yb-doping remain relatively underexplored. Focusing on a single rare-earth dopant provides a simpler and more controlled system for elucidate the relationship between Yb incorporation, structural modifications, and luminescent behavior, while minimizing the phase heterogeneities often associated with multiple or complex co-doping profiles [2,6]. This approach is particularly relevant for establishing a clear understanding of the role of Yb in modifying the structural, optical, and functional properties of HAp.

Understanding the mechanisms governing Yb incorporation into HAp lattice requires a multifaceted approach, as discrepancies may arise between idealized computational models and experimentally synthesized materials [2,11]. Theoretical approaches, such as density functional theory (DFT), typically consider defect-free crystals and may overestimate structural parameters, whereas experimental synthesis may introduce defects, microstructural disorder, lattice distortions and variations in crystallinity [2,11]. Such differences can significatively influence the local environment of the dopant and, consequently, its structural and optical properties. Therefore, integrating theoretical and experimental approaches is essential for elucidating the mechanisms of Yb incorporation and predict its performance in biomedical applications [11,12].

Therefore, this study presents a comprehensive theoretical and experimental investigation of single Yb-doped HAp (Yb-HAp), whit particular emphasis on the substitution of a Ca site by a Yb atom. By combining ab-initio calculations with experimental synthesis and characterization, this work aims to elucidate the structural, optoelectronic, and mechanical modifications induced by Yb incorporation and to stablish the relationship with the resulting material properties. The findings provide fundamental insights into the role of Yb-dopants in HAp and highlight the potential of Yb-doped HAp as a multifunctional biomaterial tailored for advanced dental applications, particularly in dental imaging and minimally invasive therapies.

2. Materials and Methods

2.1. Material Synthesis

Pure and ytterbium-doped hydroxyapatite (HAp) samples (Yb-HAp) were synthesized using the sol-gel method to ensure high molecular homogeneity. Analytical-grade calcium nitrate tetrahydrate (Ca(NO₃)₂ · 4H₂O, 1 M) and ytterbium nitrate pentahydrate (Yb(NO₃)₃ · 5H₂O, 1 M) were used as cation sources, along with ammonium diacid phosphate ((NH₄)H₂PO₄, 0.48 M) as the phosphorus source. During the synthesis process, the pH of the solution was adjusted and maintained at approximately 10.5 by the dropwise addition of sodium hydroxide (NaOH, 1 M) under constant stirring. Once the gels were formed, they were subjected to heat treatment by calcination in a muffle furnace. The temperature was raised to 400 °C at a controlled heating rate of 5 °C/min, maintaining this temperature for 3 hours to promote crystallization of the pure phases and the removal of organic residues.

2.2. Experimental Characterization

The structural and crystallographic properties of the synthesized powders were analyzed by X-ray diffraction (XRD) using a Bruker D8 Focus diffractometer operated at 40 kV and 40 mA. Diffractions were recorded over an angular range of 5° to 90° with a step size of 0.02°, and the crystallographic data were subsequently analyzed using the Rietveld refinement method. Surface morphology and qualitative elemental composition were evaluated using scanning electron microscopy equipped with energy-dispersive X-ray spectroscopy (SEM-EDS, Thermo Scientific Prisma E) operating in low vacuum mode at 10 kV with a magnification of 5000x. To evaluate the functional groups and vibrational modes of the material, Fourier transform infrared (FTIR) and Raman spectroscopy were employed. FTIR spectra were obtained using a Bruker Alpha II spectrometer equipped with a diamond ATR module, scanning in the 4000 to 400 cm⁻¹ range. Raman spectra were acquired using a Renishaw inVia micro-Raman spectrometer with a 514 nm laser as the excitation source. On the other hand, the optical properties were determined by UV-Vis spectroscopy (Biochrom Libra S22), using the Tauc plot method to calculate the band gap energy. To investigate the luminescent properties and electronic transitions of the samples, photoluminescence (PL) and cathodoluminescence (CL) analyses were performed. PL measurements were conducted in retroreflection geometry using the same Renishaw inVia micro-Raman spectrometer, utilizing He-Cd (325 nm) and a continuous-wave solid-state diode laser (785 nm) as excitation sources. Complementary CL analyses were performed using a Horiba HCL-I312 spectrometer equipped with a parabolic mirror, which was coupled to an FEI Quanta 650 scanning electron microscope. The electron beam was accelerated using voltages between 5 kV and 10 kV to optimize signal intensity and evaluate the emission related to ytterbium ions embedded in the hydroxyapatite matrix. Finally, the micromechanical properties of the samples were characterized by atomic force microscopy (AFM) and nanoindentation using a WITec alpha300RA system. Nanoindentation tests were performed to obtain force-distance curves, from which the contact stiffness (S), hardness (H_V), and elastic modulus (E) of the materials were determined from the unloading segment using the standard Oliver–Pharr method.

2.3. Computational Details

To complement the experimental findings and understand the effects of doping at the atomic level, first-principles calculations based on Density Functional Theory (DFT) were performed using the Quantum Espresso software package. Exchange and correlation interactions were described using the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Ernzerhof (PBE). For pristine HAp, standard DFT calculations were employed; however, to properly account for the strong Coulomb self-interaction of the localized $\mathrm{Yb}\text{-}4f$ orbitals in Yb-doped HAp, the $\mathrm{DFT}+U$ approach was implemented with an effective Hubbard parameter of $U=6.0\mathrm{eV}$ applied to the $\mathrm{Yb}\text{-}4f$ states. The electronic wave functions and charge density were expanded using cutoff energies of 45 Ry and 450 Ry, respectively, with Brillouin zone sampling based on a 6x6x6 Monkhorst-Pack k-points mesh. The energy surface was calculated as a function of the lattice parameters to determine the equilibrium geometry, followed by the calculation of the total and partial density of states (DOS and PDOS) and the band structure to identify the nature (direct or indirect) and magnitude of the band gap.

3. Results

3.1. Experimental Characterization

3.1.1. Structural and Morphological Analysis

Figure 1 shows the X-ray diffraction (XRD) patterns for the pure HAp and Yb-HAp samples. In both samples, the characteristic peaks of the hexagonal hydroxyapatite phase (ICDD PDF card No. 09-0432, space group P6₃/m) were identified. The experimental lattice parameters, crystallite size, and atomic site occupancies were determined using Rietveld refinement. For pure HAp, the obtained lattice values were a = b = 9.4868 ± 0.0042 Å and c = 6.9073 ± 0.0038 Å, with a mean crystallite size of 13.29 ± 0.11 nm. Following the incorporation of ytterbium, a reduction in the unit cell volume from 538.367 ± 0.561 ų to 530.853 ± 0.453 ų was observed, with parameters a = b = 9.4302 ± 0.0035 Å and c = 6.8929 ± 0.0029 Å. The crystallite size for this doped sample was estimated to be 7.04 ± 0.14 nm. Furthermore, the analysis of atomic positions confirmed the successful substitution of Ca²⁺ ions by Yb³⁺ ions, revealing that the dopant was preferentially incorporated into the Ca(II) crystallographic site with an occupancy fraction of 0.027 ± 0.007. Morphological analysis by SEM (Figure 2) revealed that both materials exhibit an irregular particle size distribution with particle sizes ranging from 0.2 to 8.5 µm for pure HAp and 0.3 to 9.0 µm for Yb-HAp. Energy-dispersive X-ray spectroscopy (EDS) confirmed the presence of Ca, P, and O in the pure sample, and the incorporation of Yb in the doped sample. Elemental quantification indicated that pure HAp is deficient in calcium, exhibiting a Ca/P molar ratio of 1.4, while the Yb-HAp sample was found to be deficient in phosphorus, exhibiting a (Ca+Yb)/P molar ratio of 1.9.

3.1.2. Vibrational Spectroscopy

The structural vibrational modes and local environment modifications resulting from Yb³⁺ incorporation were evaluated by FTIR and Raman spectroscopy.

The FTIR spectra (Figure 3) confirm the preservation of the characteristic hexagonal hydroxyapatite phase while revealing distinct spectral changes upon doping. Both materials exhibit the fundamental internal modes of the phosphate (PO₄³⁻) tetrahedra, including the asymmetric stretching ν₃ mode (1030-1090 cm⁻¹), the symmetric stretching ν₁ mode (962 cm⁻¹), the typical bending ν₄ doublet (565 cm⁻¹ and 602 cm⁻¹), and the weak bending ν₂ mode (472 cm⁻¹). However, marked differences are observed in the Yb-HAp sample: the structural hydroxyl (OH^-) stretching band at 3570 cm⁻¹ and its librational mode at 630 cm⁻¹ undergo a pronounced reduction in definition and intensity compared to pure HAp. Furthermore, as shown in the insets, the B-type carbonate (CO₃^2-) doublet at 1418-1455 cm⁻¹ is significantly attenuated, accompanied by a slight broadening of the main ν₃-PO₄³⁻ band. Crucially, the inset in the 600-1200 cm⁻¹ region reveals the emergence of an additional ν₄-PO₄³⁻ bending feature centered near 715 cm⁻¹ in the Yb-HAp spectrum, which is absent in pure HAp, signaling dopant-induced changes in the vibrational activity of the phosphate framework.

Raman spectroscopy (Figure 4) complements these findings by resolving all four active vibrational modes of the phosphate units: ν₂ (430 and 449 cm⁻¹), ν₄ (579, 591, and 608 cm⁻¹), the dominant ν₁ mode at 961 cm⁻¹, and ν₃ (1048 and 1075 cm⁻¹). The high-resolution inset focusing on the main ν₁ symmetric stretching line highlights the direct effect of the dopant: while pure HAp displays a sharp, symmetric peak at 961 cm⁻¹, Yb-HAp exhibits noticeable line-broadening together with a distinct shoulder appearing on the higher-wavenumber side (980-1000 cm⁻¹). This spectral asymmetry reflects local crystal field distortion and heterogeneous lattice strain, suggesting the substitution of smaller Yb³⁺ cations into the Ca(II) crystallographic sites and the consequent disruption of adjacent PO₄ tetrahedral symmetry.

3.1.3. Optical Properties

Optical properties were determined from UV-Vis absorbance spectra (Figure 5). Using the Tauc plot method for indirect transitions, the band gap energy was estimated. Pure HAp exhibited a band gap of 4.87 eV. In contrast, the Yb-HAp sample showed a significant reduction in the band gap, reaching a value of 3.47 eV, which indicates the formation of new localized electronic states associated with the 4f electrons of the ytterbium ion.

3.1.4. Micromechanical Properties

The microscale mechanical properties were evaluated by nanoindentation with AFM. Representative force-distance curves are shown in Figure 6. From these curves, pure HAp was calculated to have an elastic modulus of 0.166 MPa and a microhardness of 0.204 MPa. The incorporation of ytterbium induced an increase in the mechanical properties, raising the elastic modulus to 0.192 MPa, the microhardness to 0.307 MPa, and slightly improving the structural stiffness of the material (from 0.2215 N/m to 0.2267 N/m).

3.1.5. Luminescent Properties

Under UV excitation at λ_exc = 325 nm, the NIR PL spectrum of Yb-HAp exhibits a characteristic emission band in the 900–1100 nm range, dominated by a sharp peak at 974 nm accompanied by additional Stark-split component near 981 nm, ~1000 nm, and a broad band around 1040 nm (Figure 7). These spectral features correspond to the intra-4f electronic transition ${{}_{}{}^2\mathrm{F}}_{5/2}\to {{}_{}{}^2\mathrm{F}}_{7/2}$ of the Yb³⁺ ion. Upon excitation at λ_exc = 785 nm (inset in Figure 7), the characteristic NIR emission centered at 976 nm is also observed. Since 785 nm excitation is not resonant with the main Yb³⁺ 4f–4f absorption transitions, the observed emission could potentially involve excitation through defect-related states within the HAp matrix, followed by energy transfer to Yb³⁺ centers. This possibility is consistent with the presence of intrinsic defects and local structural disorder in HAp, which may introduce electronic states within the band gap. The observation of Yb³⁺ emission under both excitation wavelengths confirm the presence of optically active Yb³⁺ centers in the HAp matrix. In contrast, pure HAp exhibits only a weak, featureless background in this NIR spectral region.

The CL spectra provide further insight into intrinsic defect-related emission of the HAp host and the luminescence of ${\mathrm{Yb}}^{3+}$ ions over the 200–1200 nm spectral range. For pure HAp (Figure 8a), the CL spectrum exhibits a broad and complex emission band spanning the UV-Vis region (250–850 nm). Gaussian deconvolution of this broad emission reveals several distinct sub-bands centered at 3.95 eV (~314 nm), 3.50 eV (~354 nm), 2.96 eV (~419 nm), 2.33 eV (~532 nm), 1.91 eV (~649 nm), and 1.64 eV (~756 nm). These emission bands can be associated with radiative recombination involving intrinsic defects in the HAp lattice, such as oxygen- and calcium-related vacancies and hydroxyl-related defect centers. For the Yb-HAp (Figure 8b), the broad UV-Vis defect-related emission remains observable, although its intensity is magnified by a factor of 60 relative to the NIR region for visualization purposes. The spectrum is, therefore, dominated by an intense, narrow NIR emission band centered at 974 nm, corresponding to the ${{}_{}{}^2\mathrm{F}}_{5/2}\to {{}_{}{}^2\mathrm{F}}_{7/2}$ transition of Yb³⁺. The pronounced enhancement of the Yb³⁺ emission relative to the intrinsic host emission under electron-beam excitation suggests an efficient host-to-dopant energy transfer process. This finding indicates that the intrinsic defect states of HAp may act as intermediate excitation pathways for the Yb³⁺ centers, contributing to the population of the ${{}_{}{}^2\mathrm{F}}_{5/2}$ excited state and subsequent NIR emission, although further measurements would be required to establish the specific energy transfer mechanism.

3.2. DFT Calculations

3.2.1. Geometric Optimization and Electronic Structure

To evaluate the thermodynamic preference for Yb³⁺ incorporation, total energy calculations were performed by substituting representative calcium sites. The total energy of the system with Yb³⁺ occupying the seven-coordinated Ca(II) position was found to be lower by 0.16 eV (0.011 Ry) compared to the six-coordinated Ca(I) site, confirming that substitution at Ca(II) is energetically favored.

Full structural relaxations were performed using the variable-cell relaxation method to determine the ground-state lattice parameters of both systems. The optimized unit cell for pure HAp yielded lattice constants of a = 9.551 Å, c = 6.896 Å, and a volume of V = 544.74 ų. Upon ytterbium substitution (Yb-HAp), a noticeable lattice contraction was obtained, resulting in a = 9.380 Å, c = 6.848 Å, and V = 521.69 ų. This volume reduction is in excellent qualitative agreement with the crystallographic contraction trends observed experimentally by XRD.

To gain deeper insights into the electronic properties, the DOS and PDOS were calculated (Figure 9). Pure HAp exhibits a wide indirect bandgap of 5.19 eV, where the valence band maximum is dominated by O-2p states. For Yb-HAp, the fundamental energy gap of the host apatite matrix remains wide at 5.25 eV. However, the PDOS reveals that the localized Yb-4f orbitals introduce sharp intermediate electronic states situated directly around the Fermi level. These localized 4f level insertions effectively narrow the optical excitation threshold to approximately 1.0 eV, providing a solid theoretical justification for the apparent bandgap reduction observed in the experimental UV-Vis absorption characterization.

4. Discussion

The combined experimental crystallographic analysis and DFT variable-cell relaxations provide a consistent picture of structural contraction upon Yb³⁺ incorporation. The reduction in lattice parameters (a and c) and unit cell volume is directly driven by the ionic radius misfit between Yb³⁺ (0.985 Å for 6-coordination) and the substituted Ca²⁺ cations (1.00 Å for Ca(I) and 1.06 Å for Ca(II)) [13,14]. Energetically, our ab initio total energy calculations confirm that Yb³⁺ substitution into the seven-coordinated Ca(II) sites is thermodynamically favored over the six-coordinated Ca(I) sites by ~0.16 eV per unit cell, driven by favorable local coordination environment relaxations within the hexagonal apatite framework [4].

This heterovalent substitution (Yb³⁺ → Ca²⁺) necessitates charge compensation mechanisms within the lattice, typically achieved through the creation of calcium vacancies (2Yb³⁺ + V_Ca → 3Ca²⁺) or structural hydroxyl depletion [15]. This is directly corroborated by the attenuation and loss of definition of the OH^- stretching (3570 cm^-1) and librational (630 cm^-1) bands in the FTIR spectra. Furthermore, the substitution induces a severe reduction in local point-symmetry surrounding adjacent phosphate units, lowering the site symmetry of the ${\mathrm{PO}}_4^{3-}$ tetrahedra from C_S to C₁ [16]. This local site-symmetry breaking alters optical selection rules, leading to two notable vibrational anomalies observed in this study: 1) The activation of a new ${\nu }_4{\text{-}\mathrm{PO}}_4^{3-}$ bending mode centered near 715 cm^-1 in the FTIR spectra, which corresponds to a normally forbidden or degenerate sub-vibrational state activated by lattice strain [16,17]; 2) The spectral broadening and emergence of a high-wavenumber shoulder (980 - 1000 cm^-1) alongside the main Raman-active ${\nu }_1\left(\mathrm{P}\text{-}\mathrm{O}\right)$ stretching peak. This asymmetry reflects localized distributions of distorted P-O bond lengths and internal crystal-field gradients around the dopant sites [17,18].

Understanding the electronic structure of rare-earth doped hydroxyapatite is essential for tailoring its optoelectronic and luminescent responses. The DFT DOS calculations reveal that pure HAp behaves as a wide bandgap insulator (5.19 eV), with the valence band maximum composed predominantly of O-2p states and the conduction band minimum governed by Ca-4s states [19]. In Yb-HAp, the host matrix retains its wide fundamental bandgap (5.25 eV), preserving the optical transparency of the apatite framework. However, the PDOS demonstrates that the localized Yb-4f states insert discrete, sharp energy levels directly across the Fermi level. These localized intra-gap 4f states act as intermediate electronic steps, effectively narrowing the experimental optical absorption threshold to ~1.0 eV, as evidenced by UV-Vis spectroscopy [20]. Rather than degrading the host crystal matrix, these intermediate states serve as highly efficient excitation/emission channels for PL and CL. The sharp 4f-4f electronic transitions of Yb³⁺ (specifically ²F_5/2 → ²F_7/2) provide NIR luminescent emissions, which are biologically advantageous due to maximum light penetration through biological tissues and minimal background autofluorescence [20,21].

Hydroxyapatite is widely utilized in orthopedic coatings, bone tissue engineering, and restorative dentistry; however, pristine synthetic HAp suffers from low fracture toughness and moderate elastic moduli [22]. In the present study, experimental nanoindentation measurements demonstrate significant mechanical reinforcement upon Yb³⁺ doping, evidenced by enhanced elastic moduli compared to pure HAp. From a chemical bonding perspective, this mechanical stiffening is rooted in the shorter, more covalent Yb-O bonds formed within the distorted Ca(II) polyhedra compared to the native Ca-O ionic interactions [15,23]. The lattice contraction and higher electron charge density around the trivalent dopant increase the volumetric strain energy barrier against mechanical deformation. In dental applications (such as enamel remineralization coatings, resin composite fillers, or implant surfaces) enhanced mechanical stiffness and resistance to micro-indentation are crucial to withstand cyclic masticatory forces and prevent surface wear [23,24].

The combination of enhanced mechanical integrity, structural stability, and tailored optical properties establishes Yb-HAp as a versatile, multifunctional biomaterial for theranostic applications. While conventional HAp serves primarily as a passive structural scaffold, Yb-HAp enables real-time non-invasive bio-imaging and luminescent tracking of implant integration or drug delivery vectors alongside its load-bearing role [15,25].

Future research should focus on evaluating the in vitro and in vivo biocompatibility, cytotoxicity, and cell proliferation (e.g., human osteoblasts or periodontal ligament stem cells) of Yb-HAp to confirm its clinical safety threshold.

5. Conclusions

In summary, this study provides an atomic-scale understanding of the structural, optoelectronic, and mechanical impacts of Yb³⁺ substitution in hydroxyapatite. Trivalent ytterbium preferentially incorporates into Ca(II) crystallographic sites, triggering lattice contraction, hydroxyl depletion via charge-compensating calcium vacancies, and local point-symmetry reduction in adjacent phosphate tetrahedra. These structural alterations directly explain the strain-activated vibrational modes observed in FTIR and Raman spectra. Crucially, the introduction of intra-gap Yb-4f states tailors the optical response to enable sharp near-infrared luminescence without compromising the fundamental bandgap or structural stability of the host matrix. Coupled with enhanced elastic moduli driven by localized $\mathrm{Yb}\text{-}\mathrm{O}$ bond covalency, Yb-HAp emerges as a highly promising biomaterial for load-bearing dental composites, remineralization coatings, and non-invasive bio-imaging applications.