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Lithium Tetraborate as a Neutron Scintillation Detector: A Review

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24 November 2023

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24 November 2023

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Abstract
This review explores the potential implementation of lithium tetraborate (Li2B4O7) as a scintillator medium for neutron detection applications. Several characteristics required for the neutron detection process suggest that Li2B4O7 could be a suitable material for scintillation-based neutron detection systems. The inherently large neutron capture cross-section due to 10B and 6Li isotopes, and the ease with which Li2B4O7 can be enriched with these isotopes, combined with the facile inclusion of rare-earth dopants are all expected to improve luminescent properties as well as neutron detection efficiency of Li2B4O7. The electronic structure of doped and undoped Li2B4O7 are explored using photoemission and inverse photoemission spectroscopies, optical measurements, and theoretical computational studies such as density functional theory. The scintillation properties are further enhanced because of the wide bandgap, and transparency towards the photons that are emitted following neutron capture.
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Subject: Physical Sciences  -   Condensed Matter Physics

1. Introduction

Neutron detection is an inherent component of neutron radiation dosimetry, cross border interdiction of fissile materials [1,2], nuclear reactor fuel and nuclear safety management [3,4], nonproliferation, nuclear stockpile monitoring, and nuclear medicine [5]. These particles are uncharged, which means that neither do they provide a direct electronic signal, nor do they readily interact with most matter. In short, when compared to detection of other forms of radiation, neutron detection is nothing short of an ordeal. Therefore, when, in a Senate hearing, Dr. Robert J. Oppenheimer was asked what instrument he would use to detect an atomic bomb, his answer was "a screwdriver", implying one would have to open every container to detect fissile materials because radiation emanations were extremely small [6].
Due to above-mentioned reasons, practical neutron detection methods rely on indirect measurements based upon an initial neutron interaction producing a secondary species (conversion) that is readily measurable due to its effect on electronic and/or optical properties [7]. Neutron detectors are, therefore, divided into electronic (gas-filled or semiconductor devices where ionization leads to an induced current or voltage pulse) or scintillation (absorption of radiation followed by luminescence in the material) detectors. However, the process of selecting just the right kind of materials to manufacture reliable neutron detectors faces a colossal challenge of circumventing the background radiation. To elaborate further, background γ-ray emissions, either from natural terrestrial sources or from the γ-ray emitters associated with the neutron source, can mask the secondary ionization or excitation signal from a neutron detector as well. Thus, many applications seek materials made of the lighter elements to remove or reduce the signals that might arise from associated X-ray and γ radiation, often referred to as being “γ-ray blind” [7], meaning that a very high neutron to gamma-ray detection ratio is sought [8]. Currently, there exist six kinds of materials used as scintillators: organic crystals, organic liquids, plastics, inorganic crystals, gases, and glasses. Among these materials, crystal, glass, and gas scintillators are often used for neutron detection; however, gases are less sensitive to β (Beta) and γ (Gamma) radiation, while background from γ rays is generally higher for solids and liquids due to higher atomic density. For thermal neutrons in particular, detectors with a high concentration of 6Li are employed because they enhance the scintillation sensitivity [9], which is why lithium tetraborate (Li2B4O7) has been touted to be a highly efficient material for applications in scintillation neutron detectors [10,11,12,13].
In this review article, the crystal and optical properties of the lithium tetraborate (Li2B4O7) are described. The optical properties and photoemission characteristics are discussed in detail to understand the advantage of using this material as a scintillator neutron detector. The most important results on rare earth (RE) doping of this material and how this doping enhances the scintillation characteristics are also presented. Therefore, new research direction on scintillation efficiency and transparency can be identified through this review article. This information is critical to finally design and manufacture high efficiency and low-cost Li2B4O7-based neutron scintillation detectors.

2. Lithium tetraborate based scintillation detectors

Lithium tetraborate, usually known for its pyroelectric and piezoelectric properties [14,15,16], is a complex tetragonal crystal with 104 atoms per unit cell (see Figure 1a), with dimensions a = b = 9.470 Å and c = 10.290 Å, and a space group of I41cd. It has a characteristic wide electronic bandgap of ~9.2 to 9.8 eV [17], a large capability for thermal neutron capture, and high radiation resistivity. Li2B4O7 is also known to possess the best scintillation parameters among all the lithium borates [11,12,18,19], and multiple experimental evidence advocating the use of Li2B4O7 as a scintillator have existed for quite some time now [12].
Work by Zadneprovski et al. [11] has confirmed that undoped Li2B4O7 is in fact γ blind, that is to say largely insensitive to γ-ray radiation due to low γ-ray cross-sections, which is consistent with the fact that the primary elemental constituents of Li2B4O7 all have very low Z values. Since Li2B4O7 growth requires little post-material fabrication processing, scintillation detectors based on Li2B4O7 hold promise for an inexpensive and efficient detection system. Moreover, lightweight Li2B4O7 sheets can be combined with multiple scintillation-photomultiplier tubes into a single PIN diode (or photon sensor) so they can be scaled to large areas with little need for increased power or loss of detection area due to the need for pixelation, and concomitant device connections, as would be the case in a solid-state device. Detectors based on Li2B4O7 can therefore be made thick enough to provide the necessary neutron moderation within the detector medium, leading to higher absolute efficiency. Lastly, Li2B4O7 is fairly immune to terrestrial level temperature changes and unaffected by moisture and corrosion, making it well-suited for harsh environmental applications.
In terms of the physics of operation, the advantage of using Li2B4O7 as a neutron detection medium arises from the high thermal neutron capture cross-section inherent in the nuclear isotopes of B 5 10 (σB = 3935 barns) and L i 3 6 (σLi = 940 barns). Natural B consists of ~20% of 10B and natural Li consists of ~6% of 6Li. Luminescence is generated by electron-hole pair creation and annihilation resulting from the energetic daughter products of 10B [9] and 6Li [10] capture reactions as shown below:
  • 10B + n → 7Li (0.84 MeV) + 4He (1.47 MeV) + γ (0.48 MeV) (94%)
  • 10B + n → 7Li (1.015 MeV) + 4He (1.78 MeV) (6%)
  • 6Li + n → 3H + 4He + (4.8 MeV)
In order to improve the neutron interaction probability, Li2B4O7 can be formed using Li and B enriched with 6Li and 10B respectively [10], increasing the thermal neutron capture cross-section. Both isotopes can be enriched using standard isotopic separation techniques. And even though standard isotopic separation techniques can be applied to enhance the enrichment of both the isotopes, usually Li is more widely used than B because its neutron capture reaction products have higher energy and lead to greater light output.
Single crystal Li2B4O7 in its pure form exhibits luminescence, but the scintillation efficiency is insufficient for practical neutron detection applications [20]. Another major drawback to using Li2B4O7 as a scintillation detector is that, like many glass-based materials, it is sensitive to electron (β), proton, and α radiation. Although it is possible to use a pulse height discrimination technique to separate 6Li or 10B neutron capture events from other events, the response time is on the order of 10 ns and the light output is low, typically approximately 30% of that of anthracene [9]. In order to compensate for this disadvantage, the light output must be maximized to produce an adequate neutron capture scintillation response, obtained by select doping of the material. Fortunately, Li2B4O7 readily accepts incorporation of dopants such as Cu, Ag; as well as the rare earth elements such as Yb- [11,21], Ce- [11], Nd- [19,21], Sm- [11], Eu- [11,22], Gd- [19], Tb- [11], Er- [19] and Tm- [11,23] that enhance the luminescence by increasing recombination sites and adding luminescence lines [11,21,22,23,24,25,26,27], which increases the luminescent efficiency. Rare earth elements are especially useful as they exhibit sharp luminescence originating from their intra-4f electronic transitions [21,22,23,24,25,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49].
The partly filled 4f orbitals of the rare earth elements in conjunction with a filled 5s and 5p subshell provide enough shielding from the crystal field (electric field exerted by neighboring atoms) so that the energy levels of the rare earth ion closely resemble those of the free ions when incorporated in the Li2B4O7. This property greatly increases luminescence efficiencies, and the light output is more readily detected in a photodetector. The doped Li2B4O7 results in better linear dose response as compared to common thermoluminescent dosimeter materials (e.g., LiF), making it an attractive material for dosimetry applications [19,24,27,50]. Although many elements have been used for doping Li2B4O7, only cerium-activated lithium or borosilicate glass scintillators are well established and widely used as thermal (slow) neutron detectors [9,11,51,52,53,54]. And if the goal is to improve the sensitivity of Li2B4O7, it can be achieved by doping it with Ag [27]; besides, combining the Ag-doped Li2B4O7 with solar-blind photomultiplier can also lead to a high signal-to-noise ratio [27].

3. The Optical Characteristics of Li2B4O7

Owing to the wide electronic bandgap (~8.9 to 10.1 eV), as seen in the combined photoemission and inverse photoemission measurements [15,17], Li2B4O7 single crystals are transparent across a wide range of 165–6000 nm and the fundamental absorption maximum is located at about 133 nm [15]. In nature, Li2B4O7 occurs as a clear, colorless mineral as inclusions of diomignite in pegmatite and it can be easily manufactured into crystals or glasses. As mentioned before, it can be fabricated into large sheets using readily available manufacturing techniques, so the assembly of large area detector arrays is possible, and costs can be relatively low [50] because specialized materials processing is not required. Pure Li2B4O7 glasses, on the other hand, typically present high transparency in the range of 300–2600 nm, with three low-intensity emission bands centered at 402 nm, 520 nm, and 728 nm [11]. Regardless of whether it is a Li2B4O7 single crystal or a pure Li2B4O7 glass, addition of dopants can be expected to alter their respective luminescence spectrum.
Figure 2 presents the transmission spectra of both undoped and doped single crystals of Li2B4O7. In this figure, signatures of an apparent trade-off between luminescence and transparency, as an increase in luminescence comes at the cost of transparency and efficiency of light collection, are observed. Doping Li2B4O7 single crystals with Ag gives birth to new absorption bands at 174 nm and 205 nm (indicated by the arrows in the figure), whereas both undoped and Cu doped Li2B4O7 crystals present a broad low-intensity band [50].
Figure 3 presents the electronic band configuration of Li2B4O7 obtained from photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES). The spectra reveal several sub-band transitions. The valence band has a high intensity (or high electron density) primary peak in photoemission (below the Fermi level (EF)), and the strong feature above EF, observed in inverse photoemission, denotes the conduction band edge. A detailed analyses of the structures shown in Figure 3 unveil that the top of the valence band in a Li2B4O7 single crystal is mainly occupied by just boron-oxygen groups, while the bottom of its conduction band includes orbital contributions from lithium as well [15,56]. The energy interval between the two strong spectral features in Figure 3, one each in photoemission and inverse photoemission, represent the ground state bandgap. From these measurements [15,17] on a Li2B4O7(100) crystal, the ground state bandgap is found to be 9.8±0.5 eV, falling right in the range between 8.9±0.5 eV and 10.1±0.5 eV [15,17,55,57,58], which is somewhat in line with theoretical expectations [56]. These measured values for the ground state bandgap are higher than previously measured values of the optical gap (Eg (opt) = 7.4 eV) extrapolated from the absorption plot [15,55], but closer to the theoretical ground state bandgap. This means that incident photons possessing energy less than the ground state bandgap, determined from photoemission and inverse photoemission, can still create electron-hole pairs by exciting electrons from the valence band to the conduction band. The creation of carriers will manifest as an increase in the conductivity of the crystal, especially if the carrier mobility and lifetimes are reasonable. Such an increase in the electron population in the conduction band due to optical excitations will, in turn, amplify the photoconductivity of Li2B4O7 crystal while modifying its optical parameters. That is to say, once the Li2B4O7 crystal becomes conductive, the complex refractive index n ~ = n 1 + i χ becomes more relevant to the crystal structure model.
The overall dielectric function for all coordinate indices for Li2B4O7 can be determined via crystallographic-direction dependent density functional theory (DFT). However, bandgaps estimated from DFT are subject to error and typically produce an incorrect bandgap that is smaller than the true ground-state bandgap [59,60,61,62]. Therefore, the scissor approximation method (SOA) was applied to the real ε1(E) and imaginary ε2(E) parts of the dielectric function (shown in Figure 4). In these calculations, the scissor correction error of 1.04 eV is towards the lower end of the range specified by Rasmussen [63] of 1 to 3 eV. This error is small, producing a near identical approximation to the ground-state band gap of 7.3 eV found using the generalized gradient approximation (GGA), shown in Figure 5. Here, it must be noted that this gap of 7.3 eV is close to the ~7.4 eV gap inferred from optical transmission (Figure 2) and the band edges seen in combined photoemission and inverse photoemission (Figure 3), therefore the usage of these corrections to DFT appears somewhat reasonable. Figure 6 illustrates the calculated absorption coefficient and refractive index with and without using the scissor approximation, averaged over three directions to account for the fact that all crystal faces are not identical in their symmetry.
In addition, with the use of Sellmeier equations, the refractive index of the single lithium tetraborate crystals can be easily verified. The Sellmeier equations applied to the Li2B4O7 crystals are [64,65,66]: Preprints 91335 i001
The resulting refractive indices are plotted in Figure 7, where n 0 2 and n e 2 represent the ordinary and extraordinary part of the optical response to the incident light traversing a single lithium tetraborate crystal along the C4 axis. The curves center around a refractive index of 1.5, which matches the secondary peak seen in Figure 6. In addition, the small differences in the curves demonstrate nontrivial birefringence, with a bandgap of approximately 7.41 eV to 10.1 eV (with the calculated value being 6.37 eV) indicating an implicit correction of 1.04 eV to 3.73 eV. While 7.3 eV is close to the 7.4–7.5 eV gap determined from optical transmission (Figure 2), the band gap value of 10.1 eV is close to the ground-state gap of 9–10 eV extrapolated from the combined photoemission and inverse photoemission spectra (Figure 3).
The fact that structural distortions, in particular at the interface of Li2B4O7 single crystals, affect the electron levels in atoms was clearly demonstrated by Wooten et al. [17,57] and theory [67]. The influence of imperfections and defects in the lattice of Li2B4O7 single crystals are highlighted in Figure 8, which illustrates that the absorption edge for the Li2B4O7 glass differs substantially from that of the Li2B4O7 single crystal [66]. From this figure, it is evident that the fundamental absorption maximum for borate glass occurs at much longer wavelengths [66], i.e., lower energies, in comparison with that of the Li2B4O7 single crystal [57,66,68]. For the Li2B4O7 glass, the absorption spectrum shows an indistinct absorption edge, which is common for glassy samples since the crystallographic-direction dependent anisotropic optical properties are expected to be suppressed [69]. The electronic structure of disordered media, which include Li2B4O7 glasses, can still be reconciled with the electronic states of Li2B4O7 single crystals [19], chiefly because of the similarities in the electron energy density distributions. With this in mind, the long-wavelength shift of the absorption edge of the glass in comparison with single crystals can be explained by blurring the boundary of the electronic density of states. Moreover, the energy band model is still valid here considering that the direct inter-band transitions are forbidden, with indirect transitions of phonons and excitons occurring through mediation. A detailed discussion regarding such indirect optical transitions is presented elsewhere [70].

4. Factors Affecting Charge Production

As noted above, lithium tetraborate has a ground state bandgap of roughly 9.8 eV and a measured optical bandgap of 6.7 eV, and this significant bandgap, while improving light transmission, limits the number of electron-hole pairs created by the reaction products resulting from neutron capture. This optical bandgap corresponds to an approximate number of possible charge hole pairs of ~410,000 for the most probable reaction channel of 10B (94%), which has a much higher cross-section than 6Li. This calculation, of course, assumes that all the reaction energy is absorbed. Having said that, for a more accurate calculation a correction factor, to completely account for the production of an electron-hole pair due to the absorption of incoming radiation with an energy above the bandgap, must be included. These correction factors have been estimated to be 3.17 [71], and 3.44 [72,73] and employing the correction factor calculated by Klein [71] indicates that a 10B reaction should produce roughly 200,000 charges. Using the same logic for 6Li, approximately 416,000 charges would be produced, but recall that this advantage is reduced since it is known that 6Li has a smaller cross-section and lower elemental concentration. These numbers are, of course, not completely realistic as they are just the upper limits as not all the subsequently created electron-hole pairs will give rise to detectable scintillations. Instead, a neutron capture event near the surface (or an interface) can also result in either an incomplete electron-hole production or Auger-electron production or photoemission. Without defects or a dopants, excitonic decays are capable of producing photons well into the UV given that the optical gap is 6.7 eV while the ground-state band gap is 9.8 eV.
Convincing evidence of electron-hole pair production from neutron irradiation can be collected by considering Li2B4O7 as a capacitive detector. The electrical response of a Li2B4O7 detector to a neutron fluence is expected to result in a distinctly different pulse count while being irradiated, as compared to the background measurement. A Li2B4O7 crystal was irradiated in the radial neutron beam of a TRIGA Mark II nuclear reactor, and the operating bias was increased (or decreased) until a signal was detected. Once the operating biases were fixed upon detection of a signal, the pulse height spectroscopy data were recorded, as shown in Figure 9. The shutter to the beam was opened and then closed cyclically between 10-minute irradiation measurements and 10-minute background measurements using a multichannel analyzer. These results demonstrate an increase in conductance with neutron capture, consistent with the electron-hole pair creation from the Li and He or 3H and 4He ion tracks. Although counts were observed above the background during irradiation, there are no distinct spectral differences. This outcome indicates the background electrical noise is likely due to dielectric breakdown or an increase in conductivity due to electron-hole pair creation, much like the expected increase in conductivity due to photocarrier creation discussed above.

5. Factors affecting light production

Based upon the bandgap of Li2B4O7, scintillation is expected to produce a photon in the UV energy range. Figure 10 provides the scintillation response of undoped Li2B4O7 to α particle radiation from 241Am (Figure 10a), and neutrons plus α particles from a 239Pu source (Figure 10b). In these cases, assessing the interactions with incoming α radiation is particularly important as α particles are also among the main reaction products of the 10B or 6Li neutron capture reactions. The results shown in Figure 10 confirm that a majority of the light response falls below ~450 nm, which is largely in the UV spectrum (10–400 nm). However, it is desirable to produce visible light in order to exploit the high efficiencies of PIN diodes and photomultiplier tubes. Therefore, if highly efficient scintillator neutron detection systems are to be realized using Li2B4O7, then the neutron capture must be maximized as the bandgap is engineered to produce more transitions to a longer wavelength (i.e., in the visible range) while being unaffected by environmental factors such as temperature. One bandgap engineering option for increasing the wavelength in the light emission spectrum is through inclusion of defects into the Li2B4O7 structure. It has been shown that surface states [67,74] produce photovoltaic charging effects on the material pinning the surface potential 3.5 eV away from the conduction band minimum (see Figure 3) [75]. Therefore, surfaces states and defects can lead to scintillation in the near-visible [76,77,78], as shown in Figure 10b.
Most of the rare earths exhibit emission in the visible region, and into the near-infrared) [36,43]. Depending on the host, these transitions can be modified; however, all the electronic levels of the rare earth will remain inside of the bandgap of the host. When the rare earth takes the place of one of the atoms in the host, such sites become a trap center. The new transitions or trap energies can be observed by thermoluminescence, radioluminescence, or light output measurements. In 1996, Wojtowicz [79] used a simple band structure model to study the scintillation mechanism of a compound of the form AB3 doped with a rare earth ion and found that depending on the f-s energy promotion [79] a rare earth ion will act as an electron or hole trap. Energy calculations, based upon the f-s transition energy, propose lanthanide ions as the prime candidates to be used as activators for electron or hole traps. These ions can be used in Li2B4O7-based compounds (as shown in Figure 11) to act as outstanding activators for modification of the luminescence spectrum [79].
Not only the luminescence spectra of rare-earth-doped Li2B4O7 are affected by the kind of rare earth dopant [11,21,23,24,25,29,31,33,39,40,46,80], but is also depends on its concentration [29,80] and the growth atmosphere [33]. Preliminary work of Zadneprovski et al. [11] suggests that co-doping Li2B4O7 with Cu along with many rare earth dopant additions leads to a very efficient neutron scintillation (Figure 12) and this may set a limit on the available concentrations of activators, when managing the overall luminescence spectrum.
Rare earth elements tend to occupy the Li+ sites of Li2B4O7 [24,39,46] and the structural geometry of rare earth doped Li2B4O7, shown in Figure 13, does not change significantly with dopants. Occupation of B sites by a rare earth element is quite unlikely owing to the large difference in the ionic radii of B ions and that of the rare earth elements (and the oxygen coordination number of the rare earth). Li+ substitution is not the only consequence of rare earth doping; a few site distortions and site disorders are present as well, due to the change in the lengths of the bonds between the rare earth and surrounding atoms. X-ray absorption near edge structure (EXAFS) data have shown that bond lengths decrease with the increase in atomic number [24]. It is also known that rare earth impurities on Li2B4O7 are present in the form of trivalent (RE3+) ions [31,39,46]. Kelly et al. [24], using density functional theory (DFT), show indications of strong hybridization between rare earth states and the Li2B4O7 host. In their study [24], they used five rare earth elements: Nd, Gd, Dy, Er, and Yb; however, only the first four demonstrate overlapping of the unoccupied 4f levels of the rare earth with the conduction band of Li2B4O7 [24]. This finding is another indication that rare earth elements tend to occupy Li+ instead of B, because Li+ is bonded to the B4O7 by ionic bonds, while boron and oxygen are strongly tied via covalent bonds. The importance of understanding hybridization in scintillators cannot be emphasized enough because significant hybridization between the rare-earth states and the Li2B4O7 host can increase luminescence and decrease excited-state lifetimes.
A final challenge when adding activators to Li2B4O7 is in avoiding degradation to transparency. This is still a ripe area for research and material advancement. In experiments involving doping of Li2B4O7 with 3% Er by concentration, photo-optical characterization demonstrated no reduction in transparency, although little effort has been made to characterize its total scintillation efficiency [24]. Er, like Ce, Eu, Tm, and Yb, is a rare earth element with similar chemical behavior and, thus, other rare earth elements also appear quite promising.
The preliminary results of Kelly et al. [24] are not too surprising given the prior successes with rare-earth doping of Li2B4O7. What is still not known is the range of possible elemental concentrations or combinatory mixtures of co-doping Li2B4O7 with Cu along with other rare earth elements such as Ce, Tb, Er, and their effects on its optical and mechanical properties. In some of the cases, the optical transparency was improved while it stayed unaltered in other cases [11]. Additionally, about 80-85% of the transmission in doped Li2B4O7 is revealed to be in the range of 350 nm to 800 nm [11], demonstrating the high optical quality of the pure and doped glasses, which is quite an encouraging result (to say the least).

6. Conclusions

In conclusion, Li2B4O7 has several inherent physical, atomic, and nuclear properties that establish it as a promising candidate for a high efficiency, low-power, robust, low false-positive neutron detection medium. Although the elemental content and structure of Li2B4O7, along with the possibilities for 6Li and 10B isotopic enrichment, render it a great candidate for neutron scintillation detector material, there is still a substantial room for improvement in order to attain higher quantum efficiencies. Such a goal can be achieved by addressing the ideal doping concentration for producing higher scintillation following interactions with neutrons. As it stands, doping Li2B4O7 with either europium or copper doping is especially promising, as existing investigations indicate that they can be readily introduced into the crystal structure, barring a few minor detrimental effects to its luminescence and mechanical qualities. All things considered, it is fair to say that further experimental studies on both the scintillation efficiency and transparency of Li2B4O7 are needed.

Acknowledgments

This work was supported by Project PID2020-112507GB-I00 funded by MCIN/AEI/10.13039/501100011033, the National Aeronautics and Space Administration through grants NNX13AN16A, NNX14AL11A, and NNX15AI09H, the Defense Threat Reduction Agency (Grant No. HDTRA1-14-1-0041), Nebraska Public Power District through the Nebraska Center for Energy Sciences Research, and the National Science Foundation through EPSCoR RII Track-1: Emergent Quantum Materials and Technologies (EQUATE), Award OIA-2044049. The authors would like to thank Benjamin W. Montag, Brant E. Kananen and T. D. Kelly for their technical support.

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Figure 1. (a) The structure of lithium tetraborate (Li2B4O7) and (b) a lithium tetraborate single crystal showing excellent translucence.
Figure 1. (a) The structure of lithium tetraborate (Li2B4O7) and (b) a lithium tetraborate single crystal showing excellent translucence.
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Figure 2. Room-temperature transmission spectra of Li2B4O7 single crystals: 1- undoped; 2 -Cu doped; 3- Ag doped. Adapted from [55].
Figure 2. Room-temperature transmission spectra of Li2B4O7 single crystals: 1- undoped; 2 -Cu doped; 3- Ag doped. Adapted from [55].
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Figure 3. The intensity of the combined experimental photoemission (left) and inverse photoemission (right) data for a Li2B4O7(100) crystal along a) [011] and b) [010] as a function of the binding energy E-EF, where EF is the Fermi level. Adapted from [17].
Figure 3. The intensity of the combined experimental photoemission (left) and inverse photoemission (right) data for a Li2B4O7(100) crystal along a) [011] and b) [010] as a function of the binding energy E-EF, where EF is the Fermi level. Adapted from [17].
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Figure 4. The real ε1(E) and imaginary ε2(E) parts of the dielectric constant of a Li2B4O7 crystal for the average of the three index directions (solid lines), and then calculated after application of the scissor operator (dashed lines) to correct for the underestimated bandgap that is typical of DFT.
Figure 4. The real ε1(E) and imaginary ε2(E) parts of the dielectric constant of a Li2B4O7 crystal for the average of the three index directions (solid lines), and then calculated after application of the scissor operator (dashed lines) to correct for the underestimated bandgap that is typical of DFT.
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Figure 5. Calculated spectra of real ε1(E) and imaginary ε2(E) parts of the dielectric constant of Li2B4O7 crystal from DFT with the generalize gradient approximation (GGA). Eg represents the calculated bandgap (6.37 eV). (a) shows data for incident light E perpendicular to the z-axis, while (b) is for E parallel to z-axis.
Figure 5. Calculated spectra of real ε1(E) and imaginary ε2(E) parts of the dielectric constant of Li2B4O7 crystal from DFT with the generalize gradient approximation (GGA). Eg represents the calculated bandgap (6.37 eV). (a) shows data for incident light E perpendicular to the z-axis, while (b) is for E parallel to z-axis.
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Figure 6. Both (a) absorption coefficient and (b) refractive index are calculated before (solid line) and after the application of the scissor operator (dashed line) to correct for the underestimated bandgap that is typical for DFT calculations.
Figure 6. Both (a) absorption coefficient and (b) refractive index are calculated before (solid line) and after the application of the scissor operator (dashed line) to correct for the underestimated bandgap that is typical for DFT calculations.
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Figure 7. The refractive index as a function of energy of the incident photon.
Figure 7. The refractive index as a function of energy of the incident photon.
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Figure 8. Intrinsic absorption edge of Li2B4O7: (1) glass sample and (2) single crystal [66].
Figure 8. Intrinsic absorption edge of Li2B4O7: (1) glass sample and (2) single crystal [66].
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Figure 9. The differential pulse height spectrum obtained for a 10-minute count of background and neutron irradiated biased Li2B4O7 crystal.
Figure 9. The differential pulse height spectrum obtained for a 10-minute count of background and neutron irradiated biased Li2B4O7 crystal.
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Figure 10. Luminescent response in Li2B4O7 to α radiation from 241Am without (a) and with (b) Ag doping. Luminescent response in Li2B4O7 peaks at around 371 nm (a) but peaks at 533 nm with (b) Ag doping.
Figure 10. Luminescent response in Li2B4O7 to α radiation from 241Am without (a) and with (b) Ag doping. Luminescent response in Li2B4O7 peaks at around 371 nm (a) but peaks at 533 nm with (b) Ag doping.
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Figure 11. Energies of f-s transition for rare earth (RE=Ln in the figure) ions in their 3+ and 2+ states. The ions most likely to act as an electron (bottom curve) or hole (top curve) traps are indicated by squares. Adapted from [79].
Figure 11. Energies of f-s transition for rare earth (RE=Ln in the figure) ions in their 3+ and 2+ states. The ions most likely to act as an electron (bottom curve) or hole (top curve) traps are indicated by squares. Adapted from [79].
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Figure 12. The neutron pulse height spectra (1) taken from a Pu(Be) source (●) compared to γ radiation (2) from a 60Co source (o) and background (3,▼) from various doped and undoped lithium tetraborates. Adapted from [11].
Figure 12. The neutron pulse height spectra (1) taken from a Pu(Be) source (●) compared to γ radiation (2) from a 60Co source (o) and background (3,▼) from various doped and undoped lithium tetraborates. Adapted from [11].
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Figure 13. Structural model of the rare earth-doped Li15B32O56. Oxygen (red), boron (light pink), lithium (purple), and RE (green). Modified from [24].
Figure 13. Structural model of the rare earth-doped Li15B32O56. Oxygen (red), boron (light pink), lithium (purple), and RE (green). Modified from [24].
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