Rare earth dopant (Nd, Gd, Dy, and Er) hybridization in lithium tetraborate

The four dopants (Nd, Gd, Dy, and Er) substitutionally occupy the Li⁺ sites in lithium tetraborate (Li₂B₄O₇: RE) glasses as determined by analysis of the extended X-ray absorption fine structure. The dopants are coordinated by 6-8 oxygen at a distance of 2.3 to 2.5 Å, depending on the rare earth. The inverse relationship between the RE-O coordination distance and rare earth (RE) atomic number is consistent with the expected lanthanide atomic radial contraction with increased atomic number. Through analysis of the X-ray absorption near edge structure, the rare earth dopants adopt the RE³⁺ valence state. There are indications of strong rare earth 5d hybridization with the trigonal and tetrahedral formations of BO₃ and BO₄ based on the determination of the rare earth substitutional Li⁺ site occupancy from the X-ray absorption near edge structure data. The local oxygen disorder around the RE³⁺ luminescence centers evident in the structural determination of the various glasses, and the hybridization of the RE³⁺ dopants with the host may contribute to the asymmetry evident in the luminescence emission spectral lines. The luminescence emission spectra are indeed characteristic of the expected f-to-f transitions; however, there is an observed asymmetry in some emission lines.

Introduction

Materials containing boron investigated for solid state neutron detection [1] include semiconducting boron carbide [1–12], boron nitride [13–15], boron phosphide [16–19], Mg₂B₁₄ [20] and lithium borates [21–27]. In particular, undoped lithium tetraborate (Li₂B₄O₇) is capable of being enriched with ⁶Li up to 95% and ¹⁰B up to 97.3% [26], well above the natural abundances (⁶Li–7.42%, ¹⁰B–19%), thereby increasing thermal neutron capture [1, 21, 26].

Many rare earth (RE) ions exhibit high luminescence efficiency in host borate crystals and glasses with various chemical compositions [27–46]. Consequently, combining rare earth dopants with the high thermal neutron capture cross-sections of ⁶Li and ¹⁰B may result in highly efficient neutron scintillators [26, 27, 46, 47]. In lithium tetraborate, this is particularly true as undoped Li₂B₄O₇ has a wide band gap of ~9.8 eV, based on measurements of {100} and {110} oriented single crystals [24, 48–51] and is highly transparent in the visible spectrum. In general, the borates, including lithium tetraborate (Li₂B₄O₇) single crystals, are characterized by high optical transmission from far infrared to vacuum ultraviolet [49, 52].

Obtaining single crystal Li₂B₄O₇ is technologically challenging; thus, application to large area scintillation detectors will favor glasses over single crystals due to lower fabrication costs. The very low crystal growth velocity and high melt viscosity lead to difficulties with dopants, particularly rare earths [53, 54]. Therefore, from the technological viewpoint, the vitreous Li₂B₄O₇ compounds are more advantageous when compared with their crystalline analogs.

Padlyak, Teslyuk and coworkers studied the luminescence properties of some rare earth doped lithium tetraborate (Li₂B₄O₇:RE) glasses [39, 41]. They deduced from the optical characteristics that the rare earths generally occupy the Li⁺ site exclusively in the +3 valence state. Compared to other rare earth doped borates and crystalline counterparts, a broadening of the spectral lines was observed which was theorized to be a result of the dopant interaction with a varying O-coordination environment in the glassy material. Studying this varying O-coordination structure is not ideal [55] with traditional bulk diffraction measurements (e.g., XRD) due to the lack of long range order. Instead, a more localized probe such as extended X-ray absorption fine structure (EXAFS) may be used.

In this research, lithium tetraborate glasses have been separately doped with four different rare earth elements: Nd, Gd, Dy, and Er. The local environment about the dopants was studied with EXAFS in order to determine the positional disorder of the varying O environment, an average coordination number and bond length, and to assist in validating the presumption that a varying O-environment is the source of the spectral line broadening. Further, the experimentally determined site has been used as a basis for density functional theory (DFT) calculations to investigate the electronic nature behind the spectral line broadening observed in the emission spectra.

Materials and Methods

The doped Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er glasses were obtained in the air from corresponding polycrystalline compounds according to standard glass synthesis. For solid state synthesis of the doped materials, highly pure carbonate (Li₂CO₃) and boric acid (H₃BO₃) were used. Solid-state synthesis of the doped Li₂B₄O₇:RE compounds was carried out using a multi-step heating process that follows the reaction sequence [39, 41]:

$\begin{array}{l}{\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+H}}_{\text{3}}{\text{BO}}_{\text{3}}({\text{150}}^{°}\text{C},{\text{H}}_{\text{2}}\text{O}\uparrow )\\ \to {\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}\text{+}\alpha {\text{-HBO}}_{\text{2}}({\text{250}}^{°}\text{C},{\text{H}}_{\text{2}}\text{O})\to \\ \to {\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+B}}_{\text{2}}{\text{O}}_{\text{3}}({\text{600}}^{°}\text{C},{\text{CO}}_{\text{2}})\to \\ \to {\text{Li}}_{\text{2}}{\text{B}}_{\text{4}}{\text{O}}_{\text{7}}\text{+}[{\text{Li}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+B}}_{\text{2}}{\text{O}}_{\text{3}}]\to \\ \to ({\text{800}}^{°}\text{C},{\text{CO}}_{\text{2}})\to \\ \to {\text{Li}}_{\text{2}}{\text{B}}_{\text{4}}{\text{O}}_{\text{7}}\end{array}$

The Nd, Gd, Dy, and Er impurities were added as RE₂O₃ (RE= Nd, Gd, Dy, and Er) in amounts of 0.5 and 1.0 mol. %. Large doped glasses were obtained by fast cooling of the corresponding melt that was heated more than 100 K higher than the melting temperature for excluding the crystallization processes. Samples were cut for optical measurements and polished to a size of approximately 5 × 3 × 2 mm³.

Optical absorption spectra were recorded at room temperature with a Varian spectrophotometer (model 5E UV–VIS–NIR). Emission and luminescence excitation spectra were acquired with a Dongwoo (model DM711) scanning system consisting of an excitation monochromator with 150 mm focal length and emission monochromator having 750 mm focal length equipped with a photomultiplier and an InGaAs detector.

The Li₂B₄O₇:RE extended X-ray absorption fine structure (EXAFS) spectra were measured using a double crystal monochromator of Lemonnier type [56] at the DCM and WDCM beamlines located at the Center for Advanced Microstructures and Devices (CAMD) [57–59]. Due to the thickness of the glass samples and low dopant concentrations (nominally 1%), the absorption spectra were measured in fluorescence mode and the spectra analyzed without self-absorption corrections. For all samples, the L3 (2p_3/2) edge fluorescence was measured corresponding to the M5-L3 (3d_5/2–2p_3/2) transition and was found to be in reasonable agreement with expectations [60].

The EXAFS spectra were analyzed in two different ways. First, the spectra were analyzed using standard procedures with the IFEFFIT tool suite and FEFF 6 [61–65]. This consisted of isolating the EXAFS signal, converting to k-space, then using the Fourier transform to determine the average coordination number and element-type around the rare earth dopants, as detailed elsewhere for other doped Li₂B₄O₇ crystals [66] and glasses [67]. The second method of analysis employed the use of a Latin hyper-cube sampling (LHS) routine and the scattering code FEFF 9 for phase shifts and backscattering amplitudes. This code was developed as a bridge between a Monte Carlo modeling approach and traditional EXAFS fitting and is a more recent development. The power of this latter approach lies in the ability to cover a very large parameter space in modeling the experimental data and locating false minima in the fits to the data. The results of both analysis methods are generally in agreement, although the Latin hyper cube (LHS) approach is computationally faster.

Despite the glassy nature of the samples that may result in positional disorder around the RE dopant, the model used for fitting the EXAFS was based on the known crystal structure (Figure 1) of Li₂B₄O₇ [49; 55, 68–69]. This was an appropriate starting point for analyzing EXAFS spectra that will on average reflect the coordinating environment, including an average distance to the first shell and an average coordination number. As it is hypothesized that the rare earth dopants will substitutionally dope for the Li⁺ atoms, starting with the crystalline model and then adjusting the O environment to reflect the average coordinating environment makes the most sense. Furthermore, due to the low Z nature of the glassy matrix, it is expected that the photoelectric backscattering signal will be very weak beyond the first shell, unless there is significant dopant clustering in the material, which would result in a detectable RE-RE scattering shell.

FIGURE 1

Figure 1. The undoped lithium tetraborate unit cell. The 104-atom-unit cell consists of bridging BO₃ and BO₄ complexes [63, 64], with Li⁺ ions distributed throughout.

Optical Absorption and Luminescence

High-quality scintillation is dependent upon significant quantum efficiency while retaining optical transparency [27, 43–47]. For energies less than 3.3 eV (wave lengths longer than 375 nm) the absorption is low [26, 27, 49, 70, 71] and the optical absorption spectra of the investigated glasses are dominated by absorption bands of the Nd³⁺, Gd³⁺, Dy³⁺, and Er³⁺ centers and can be generally assigned to the appropriate electronic f to f transitions, as illustrated for the doped Li₂B₄O₇:Nd glass in Figure 2.

FIGURE 2

Figure 2. The optical absorption spectrum of Nd³⁺ centers in Li₂B₄O₇:Nd glass.

Although the luminescence emission spectra are characteristic of the f to f transitions of the +3 rare earth ions, the effect of the host matrix plays a role. In the case of the Nd³⁺ centers, where four characteristic f to f transition bands due to the ⁴F_3/2 → ⁴I_9/2, ⁴F_3/2 → ⁴I_11/2, ⁴F_3/2 → ⁴I_13/2, and the ⁴F_3/2 → ⁴I_15/2 dipole transitions (some shown in Figure 3) combine to provide a net quantum efficiency of 24%, inhomogeneous broadening of spectral lines does occur [72, 73]. We know that the rare earth states will couple to the host matrix, as clearly demonstrated for rare earth doped GaN [74]. As with prior studies [41], the rare earth ions are placed in the Li⁺ site but there is positional disorder of the RE³⁺ luminescence centers in the Li⁺ sites of the Li₂B₄O₇ lattice and this is characterized by slightly different spectroscopic parameters compared to other rare earth doped borates and crystalline counterparts. EXAFS studies of the L3 edge indicate that the local structure (first coordination shell) around the rare earth ions in glassy lithium tetraborate samples is closely similar. This similar result was observed in the EXAFS study of rare earth impurities on crystal and glass samples of the CaO–Ga₂O₃–GeO₂ system [75]. The structural studies must be understood in this context.

FIGURE 3

Figure 3. The luminescence emission spectrum of Nd³⁺ in Li₂B₄O₇:Nd glass.

Extended X-Ray Absorption Fine Structure

In Figure 4, the normalized experimental XAFS signal is plotted for Li₂B₄O₇:Nd. All the rare earth doped samples of this study, Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er, have very similar XAFS spectra (Figure 4 inset), including the presence of the sharp white line: a strong feature just above the absorption edge. The measured L3 edge for the Li₂B₄O₇:Nd was determined to be 6212 eV by identifying the inflection point on the rising photoelectric edge, or about 4 eV greater than the expected 6208 eV [60]. This shift in the dopant core level absorption edge is typical of lithium tetraborate and in some cases has been attributed to the large band gap of this oxide, even when doped [66] (although such a shift is commonly related to the charge on the absorbing element – a rare earth in this case). This shift in the L3 absorption edge is similar for all the data obtained for all four of the rare earth doped Li₂B₄O₇ glass samples.

FIGURE 4

Figure 4. X-ray absorption fine structure spectrum of Li₂B₄O₇:Nd. The absorption coefficient was measured for the L3 edge from 100 eV below the edge to approximately 500 eV above the edge. In addition to the X-ray absorption fine structure, a vertical line is shown at 6208 eV, which is at a smaller value than the experimental edge found to be 6212 eV. In the inset, the X-ray absorption fine structure spectra for all four samples (Nd, Gd, Dy, and Er) are plotted, shifted by their absorption edge energies so that they are centered at 0 eV to compare them directly.

In Figure 5, the experimental EXAFS spectra have been extracted from the data in Figure 4, taken above the rare earth dopant L3 edge, have been replotted as a function of wave vector k for the Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er glass samples. In all cases, the EXAFS is evident up to approximately 6 Å⁻¹ and is similar for the rare earth doped lithium tetraborate samples studied, with only small shifts. The signal-to-noise in the EXAFS spectra deteriorate with wave vectors greater than about 7.5 Å⁻¹ as is expected for glassy samples when the host matrix about the dopant consists primarily of low Z material [55, 67]. The energy range available for the various EXAFS spectra is limited by the presence of the L2 edge; hence, higher Z elements have a wider EXAFS energy range.

FIGURE 5

Figure 5. The k² weighted extended X-ray absorption fine structure taken above the L3 rare earth dopant edge for Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy and Li₂B₄O₇:Er.

The rare earth doped lithium tetraborates are very similar in structure, as is evident from the EXAFS spectra in Figure 5. The similarity in the EXAFS features for all the samples is an indication that the rare earths dope the Li₂B₄O₇ lattice in a similar fashion. This is expected, as nearly all lanthanides adopt the +3 valence state [27–47]. In spite of the similarities of the spectra obtained for the Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er glass samples, there are small shifts in wave vector placement of the EXAFS oscillations with increasing atomic number. This characteristic shift in the EXAFS features corresponds to smaller bond lengths with increasing atomic number (lanthanide contraction); larger wave vector components correspond to smaller bond lengths in the Fourier transformation to R-space.

The reliability of the structural information from our EXAFS data is limited in scope to the first coordination shell due to the signal-to-noise deterioration. Furthermore, the structural information is an indication of the average environment due to the glassy nature of the lithium tetraborate host. The Fourier transformed EXAFS spectrum for Li₂B₄O₇:Nd is plotted in Figure 6. The Fourier transformed EXAFS is typical for all the rare earth doped glass samples studied: Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er. The out-of-phase real and imaginary components of the R-space signal (plotted in Figure 6) demonstrate the high level of confidence that may be placed in the Fourier transform.

FIGURE 6

Figure 6. The Fourier transformed extended X-ray absorption fine structure signal (solid) for Li₂B₄O₇:Nd plotted in Figure 5. The real (long dash) and imaginary (small dash) components are plotted to show Fourier transform contributions. In the inset, the Fourier transform imaginary components for Nd, Gd, Dy, and Er are shown. There is a trend from left to right in the inset, with the left most (small dash) line resulting from the Er doped sample and then as the atomic number decreases the peak position moves to longer bond length (Er → Dy → Gd → Nd) with Nd as the right most (solid) line.

In the inset of Figure 6, the imaginary component for the Fourier transforms of the data of Figure 5 are plotted for all the doped samples. Traditionally, peaks in the imaginary spectra for EXAFS transforms have been correlated to physical distance in the radial distributions. Figure 7 is provided to show the quality of the EXAFS fit results and is indicative of the RE located substitutionally in a Li⁺ site. Although all the fits are not exact, this and the extracted coordination numbers are an indication of multiple interactions being measured coherently. If each interaction was known exactly, then a multiple-FEFF calculation could be made and different weights applied to each in order to determine an exact fit. Figure 7, nonetheless, demonstrates that the fits, despite deficiencies, are acceptable for all of the studied doped glass samples. The bond length contraction is noticeable with increasing Z, matching with the inset of Figure 6. The fit quality may be determined from the fitting parameters given in Table 1 for both the standard fitting method and using the LHS routine. For this result of the rare earth dopant substituting in a Li⁺ site, the greater charge of the RE³⁺ dopant may be easily compensated by anion vacancies, (V_Li)⁻ and (V_B)³⁻, elsewhere in the glassy matrix.

FIGURE 7

Figure 7. Plotted are the R-space Fourier transformed extended X-ray absorption fine structure signals for Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy and Li₂B₄O₇:Er. The vertical dotted lines indicate the fitting window used for the backward Fourier transform range (1.3–4 Å). The primary peak is the first coordination shell, comprised of O atoms.

TABLE 1

Table 1. Tabulated are the final fit parameters for the four rare earths analyzed including coordination number N, extracted photoelectric edge shift E_o, the first shell bond length R(Å) and σ² which is the mean squared displacement in the rare earth to oxygen bond length, often referred to as the EXAFS Debye-Waller factor.

Due to the size and oxygen coordination number of the rare earths, placement of a rare earth dopant in the B complexes can almost immediately be excluded. A rare earth substitution for the B atom sites would result in a very large distortion of the lithium tetraborate lattice that does not fit with our experimental EXAFS data. Table 1 supports our position as to why a rare earth in a B substitution site can be neglected. To have a rare earth substitute for B in either the BO₃ or BO₄ clusters would result in coordination numbers of 3 and 4, less than the observed 7–10 oxygen coordination obtained from the EXAFS data. The RE-O bond length is reduced if placed in a boron site, even in the best fit to the EXAFS data. In the case for Nd, the Nd-O bond length is 1.92 Å for a boron site, still significantly less than the 2.7 Å observed, but this fit (Table 1) to the EXAFS data requires an unphysical shift in the adsorption edge, as discussed below in the context of our near edge X-ray absorption experimental data. It is noteworthy that for Nd substituting for boron in the BO₃ structure, the fit to the EXAFS data would still require a expansion of the bonding distance from the B-O approximately 1.3–1.9 Å, which would greatly distort the interlocking BO₃-BO₄ portions of the unit cell. In general, substituting a rare earth element such as Nd with a radius of roughly 1.123 Å with a coordination number of 6 into a site where the B³⁺ radius is, on average, 0.15–0.25 Å for oxygen coordination numbers of 3 and 4 respectively, is unphysical. Substituting a rare earth element, such as Nd, in a manner that would in a way that would result in a bond length of 1.273 to 1.373 Å, so as to achieve less distortion of the interlocking BO₃-BO₄ portions of the unit cell, is possible only if we ignore the obvious problem of coordination number mismatch and the very large resulting charge distributions, as partly elaborated by theory below.

X-Ray Absorption Near Edge Structure

In Figure 8, the experimental X-ray absorption near edge structure (XANES) region for Li₂B₄O₇:Nd has been plotted in more detail than in Figure 4. The solid black line is the experimental data and the dotted red line is the theoretical calculation using FEFF 9.05 and full metal scattering with a cluster size of 5.1 Å and a small convergence factor of 0.05. The Hedin-Lundqvist to ground state exchange correlation was used.

FIGURE 8

Figure 8. Plotted is the experimental data (solid black line) for Li₂B₄O₇:Nd in the nominal X-ray absorption near edge structure region. FEFF 9.05 has been used to calculate a theoretical X-ray absorption near edge structure spectrum (red dotted line) using full multiple scattering. The theory has been shifted to higher binding energy by 2.8 eV (reflective of the +3 charge of the Nd dopant).

Peak fitting to the XANES data was accomplished by using an arctangent function to represent the bare atom absorption background and two Voigt functions to fit the peaks. The results are listed in Table 2. Two broad peaks are identified in the XANES spectra; one at approximately 4.00 eV beyond the experimentally determined core binding energy (6212 eV) and the other at approximately 37.57 eV above the core L3 edge. A similar peak structure is observed in a rare earth oxygen environment in Joseph et al. [76], where the broad peak at around 35 eV has been associated with nearest neighbor scattering. The other rare earth doped glass samples Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er provide similar results in spite of the differences in the placement of the L3 edge. Additionally, using the Nd doped sample as a reference, the total yields of each of the respective peaks were compared to one another and indicate similar absorption. If the total area/yield is associated with an unoccupied density of states, then there is no detectable (at least in these sample conditions) difference between the doped samples. In fact, compared to the yield, the first peak has an average ratio of 1.04 and the second 0.99, hovering just around 1 and indicating that the electronic density of states are nearly the same for all of the rare earth doped glass samples. This conclusion is consistent with strong hybridization of the unoccupied rare earth 5d states with the host Li₂B₄O₇ and thus consistent with our model electronic structure calculations discussed below.

TABLE 2

Table 2. Tabulated are the results for fitting the XANES region of the doped samples with an arctangent function and two Voigt functions.

For rare earth materials where the rare earth atom is in the +3 valence state, the XANES spectra have a single peak white line, whereas for RE elements that adopt the +4 valence state (e.g., Ce and Pr), the XANES spectra typically have a double peaked white line which occurs due to additional interactions with the ligand environment [77]. In this case, as has been discussed at length in other rare earth dopant systems literature [74, 76–82], the p → s and p → d transitions should be stronger than p → f, although the latter is not strictly forbidden if there is strong 4f state hybridization with the unoccupied band structure [74, 81–83]. In this case, the large white line peak may be associated with 2p → 5d transitions, typical of the +3 rare earth ion and similar to the Eu in doped borate glasses as in Shimizugawa et al. [78]. Placement of a rare earth (e.g., Nd) in a boron site, in the most realistic fit to the EXAFS data (as noted above), presents a huge problem for the XANES data. Such a placement of the rare earth would require an absorption edge shift of about 30 eV instead of the roughly 0 to 3 eV for substitution into a lithium site (Table 1), and it is the latter that is close to the 4 eV absorption edge shift observed, as seen in Figure 4.

Density Functional Theory Studies of RE Doped Lithium Tetraborate

To better ascertain the role the host matrix does play in the f to f transitions of the +3 rare earth ions in doped lithium tetraborate, we modeled the electron structure of Li₂B₄O₇ doped with Nd, Gd, Dy, Er and Yb. Our calculations are carried out within density function theory (DFT) as implemented in the CASTEP software [84]. The plane wave basis set with an energy cutoff around 360 eV, an ultra-soft pseudopotential, and the local density approximation for the generalized gradient approximation (GGA) and Perdew-Burke-Ernzerhof (PBE) exchange and correlation functional are employed [85]. The DFT+U method was used for the corrections of on-site Coulomb interactions with U = 6 eV. These computational conditions were previously found to be successful with rare earth doped GaN studies [74]. In addition, we utilize the ensemble density functional theory (EDFT) [86, 87] scheme in CASTEP to overcome the convergence problem inherited in the RE system. In the Da Silva et al. [88], density functional theory calculations for CeO₂ and Ce₂O₃ found that Perdew-Burke-Ernzerhof plus a scalar Hubbard U approach (PBE+U) worked reasonably well, with results similar to the Heyd-Scuseria-Ernzerhof hybrid functional (HSE). For example, PBE+U and HSE predict CeO₂ to be an insulator with the band gaps 5.3 and 7.0 eV respectively compared to the experimental value of 6.0 eV. The calculated the energy difference between the lowest 4f state and the vacant conduction band (E_g−f) of Ce₂O₃ were found to be 2.6 eV (PBE+U) and 2.5 eV (HSE) compared to the experimental value of 2.4 eV [88]. Our approach is very much the same as that PBE+U approach in the work of Da Silva and coworkers [88] except we used U = 6.0 eV for the 4f states of Nd, Gd, Dy, Er, and Yb, instead of the U = 4.5 eV for the Ce 4f used in Da Silva et al. [88]. The band gap for undoped lithium tetraborate has been estimated [89], by the above DFT approach, to be 6.48 eV, much less than the experimental value of 9.8 eV found in combined photoemission and inverse photoemission [48, 49, 89]. This is not surprising as the band gaps found in density functional theory of Li₂B₄O₇ are generally observed to the underestimates of values obtained from combined photoemission and inverse photoemission experiments [48, 49, 89].

We built a cubic cell of Li₁₆B₃₂O₅₆, as shown in Figure 9. Based on our EXAFS results that place the RE dopant in a Li⁺ site, one Li⁺ atom is then substituted by a Nd, Gd, Dy, Er, or Yb atom, representing 6.25% atomic doping which is much higher than the experimental level, but computationally tractable. Monkhorst-Pack [90] 2 × 2 × 2, k-points grids were adopted for Brilliouin zone sampling. Geometry optimizations were performed for the coordinates of the atoms and the lattice parameters until the maximum force on the atoms was less than 0.01 eV/Å, confirming slight strain in the lattice in the vicinity of the rare earth dopant and dependent on the choice of the rare earth dopant. There is strong evidence of rare earth state hybridizations with the lithium tetraborate host, while the boron and oxygen are connected by valence bonds, but Li and borate are connected through ionic bonding, as is common in density functional calculations of lithium tetraborate [49–51] and is evident in the overlap of the partial density of states as plotted in Figure 10. This indicates that the Li⁺ site is also the most reasonable choice for substitutional rare earth dopants, because the borate B₄O₇ are mostly tied by strong covalent bonds, so a rare earth dopant is very unlikely to replace either B or O. The Li⁺, on the other hand, is bonded to the borate primary through ionic bonds, which is evident from the partial densities of states of Li₂B₄O₇. Thus we feel that it is legitimate to substitute some of the Li⁺ by the rare earth atoms. In previous work [89], we noted that the Mulliken bond population, which is a measure of overlap charges in the chemical bonds [91, 92] of B-O bond is about 0.58 to 0.82, whereas Li-O bond is less than <0.06. From this one can deduce that the B-O bond is in nature strongly covalent, and Li-O is most likely ionic. The bond lengths of the B-O and Li-O are 1.36–1.51 Å and 1.97–2.46 Å, respectively, the latter being a much better fit to the EXAFS data discussed above, for substitutional rare earth doping.

FIGURE 9

Figure 9. The schematic of the structural geometry for Li₁₅B₃₂O₅₆RE (RE = Nd, Gd, Dy, Er, or Yb). Oxygen (red), boron (gray), lithium (blue), and rare earth (green) are indicated.

FIGURE 10

Figure 10. The band structure and density of states of Li₁₅B₃₂O₅₆Nd (A), Li₁₅B₃₂O₅₆Dy (B), Li₁₅B₃₂O₅₆Er (C), Li₁₅B₃₂O₅₆Yb (D). In band structure plots vs. wave vector, spin up is black and spin down is red, while in the density of states plots the rare earth d state densities are blue, f state densities are red and boron p state density is green while the total density of states envelope is black. The density of states are plotted spin resolved.

In Li₂B₄O₇:Nd (Figure 10A) and Li₂B₄O₇:Dy (Figure 10B), we observe that nearly all the unoccupied 4f levels hybridize with the lithium tetraborate conduction bands. This could explain the similarity of the edge shift uncovered by the Latin hyper cube sampling (LHS) analysis summarized in Table 1 between Nd and Dy doped samples. We find that in Er the 4f levels, particularly the spin down component situated at E_F do not mix with the host lithium tetraborate, whereas at 2–4 eV above E_F, the f state population is very low (Figure 10C). For Li₂B₄O₇:Yb (Figure 10D), there are few unoccupied 4f states, which leads to little depletion of the Yb 4f¹⁴ occupancy, unlike GaN:Yb [74]. For Nd (Figure 10A), Dy (Figure 10B), Er (Figure 10C), and Yb (Figure 10D) there is a significant 4f partial density of states that shows up within the lithium tetraborate band gap, but this is not observed for Li₂B₄O₇:Gd. We find that the occupied Gd 4f states are embedded deep at the bottom of the valence band of the Li₂B₄O₇:Gd valence band. The differences in the Gd electronic 4f state are also reflected in Table 1 from the experimental edge shift E₀ being very different from the other doped samples. Overall we interpret the rare earth 4f state placement and the clear rare earth 4f hybridization to the lithium tetraborate lattice as contributing to the f to f transition spectral broadening, similar to our expectations for Er doped GaN due to the strong hybridization of the GaN matrix with the imbedded Er 4f states [74]. Such 4f states, as calculated here, do give rise to states within the band gap, not only as plotted in Figure 10, but are seen as sharp absorption lines in the transmission spectra at wave lengths greater than 375 nm, as well as reflected in the luminescence spectra of rare earth doped lithium tetraborates [27, 72, 73].

The correlation U has been applied, as noted, to the rare earth 4f orbitals only, the remaining various orbital subset of orbitals may in some cases have applicable correlation energies as well. There is no a priori exclusion of multiple correlation energies, nor of wave vector dependence of the various possible correlation energies and such complications might well exist. This could lead to an incomplete (or insufficient) description of orbital hybridization effects including the luminescent and optical properties. In general, the increased hybridization will decrease excited state lifetimes and increase luminescent spectral feature widths, including the f to f transition spectral features. The contributions to f to f transition spectral broadening, nonetheless, arising from the strong rare earth hybridization with the lithium tetraborate lattice, are significant even without considering the variations in oxygen coordination, although Li₂B₄O₇:Yb (Figure 10D) may be the exception. The variations in oxygen coordination evident from the EXAFS, and expected for a glassy lithium tetraborate, will be even more significant because of the strong rare earth hybridization with the lithium tetraborate lattice, affecting the f to f transition spectral broadening to a great degree.

Conclusion

Previous studies of rare earth doped lithium tetraborate glasses revealed asymmetry in the RE 4f spectral emission lines. In order to determine the source of the spectral line distortion, X-ray absorption fine structure studies were conducted in order to extract the local environment surrounding the rare earth dopants. The near edge absorption spectra data analysis indicates that for all of the rare earth doped samples studied (Li₂B₄O₇:Nd, Li₂B₄O₇:Gd, Li₂B₄O₇:Dy, and Li₂B₄O₇:Er), the dopant substitutes into the Li⁺ ion sites as RE³⁺. The empirically determined site was then used to perform a density functional theory calculation and determine the electronic source of the asymmetry in the spectral emission lines.

As a result of the doping, there is a slight expansion of the coordination shells (O and B atoms) that surrounded the original Li⁺ atom from approximately 2.0 Å to approximately 2.5 Å, the exact value depending upon the size of the rare earth. The results for rare earth doped borates compare well with expected bonding distances when compared with rare earth coordination number and atomic radii from Shannon [93], the radial distributions functions obtained from X-ray diffraction [55] and consistent with prior EXAFS studies [66, 67]. The first coordination shell's distance and coordination number (in the range of 6–8) (amplitude reduction factor fixed at 0.85) compares well with the expectations for a rare earth oxygen coordination environment and occupation of the Li⁺ site. Since these are an average coordination number and coordination distance in the glass samples, it is expected that there are hypo- and hyper- environments throughout the glass that average out.

A qualitative XANES analysis confirms a +3 valence state and is consistent with our theoretical expectations. The resulting density functional theory calculations indicate there is strong hybridization with the unoccupied 4f orbitals with the host lithium tetraborate matrix. This hybridization is a likely the source of the spectral emission line distortion observed when the glass oxygen positional disorder is also taken into account.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

This work was supported by the Nebraska Public Power District through the Nebraska Center for Energy Sciences Research competitive grant program, the Defense Threat Reduction Agency (Grant No. HDTRA1-07-1-0008, HDTRA1-09-1-0060, and BRBAA08-I-2-0128), the NSF through the “QSPINS” MRSEC (DMR-0820521) at UNL. The views expressed in this article are those of the authors and do not reflect the official policy or position of the Air Force, Department of Defense or the U.S. Government.

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