1. Introduction

Optical materials based on rare earth activation center, such as neodymium and europium ions, are critical for a wide range of applications including phosphors [1–3], lasers [4], and scintillator materials [5, 6] for ionizing radiation detection [7]. Their optical properties are very sensitive to the host lattice, i.e., crystal field strength, covalency, cation size, etc., and therefore considerable attention has been paid to the search for host materials with high performance and reliability. Many of the recently developed hosts are halides [6, 8–14]. They provide high light output and reasonable scintillation decay time, but suffer from sensitivity to moisture and low mechanical strength, which has substantially limited their applications, especially as scintillators. Oxide ceramics, on the other hand, possess high chemical stability and high transparency, and thus can be ideal candidates for the next generation of scintillator materials. For example, it was recently reported that Eu-doped garnet (Y₃Al₅O₁₂) scintillators show very promising scintillation properties [15]. The widely available α-Al₂O₃ has also been considered for cryogenic phonon detector designated for the Dark Matter experiment [16, 17]. Indeed, these materials can also provide good mechanical properties, excellent refractory character, high chemical stability and optical transmission over a wide range of wavelengths.

However, efficient identification of high-performance host oxide with proper fabrication conditions is challenging. The chemical state of many rare earth activation centers (i.e., valence) is sensitive to the synthesis condition, and this is coupled with the stringent sintering conditions required to achieve transparency in polycrystalline oxide materials. Predictive method based on computations are also lacking, due to the difficulty in accurately capture the electronic behavior, particularly for the f-electrons, in different atomic environments, at realistically low doping concentration (tenths of a percent), and as a function of experimental conditions. It is therefore no surprise that determining the correct experimental conditions so far has been largely relying on trial and error. In this paper, we present a protocol to use ab-initio simulations based on density functional theory (DFT) to guide the experimental synthesis of rare earth doped transparent polycrystalline ceramics. Using Eu²⁺ doped α-Al₂O₃ as an example, we present the evidence that sophisticated DFT simulations can provide critical guidance for assessing experimental feasibility and selecting effective synthesis conditions. This provides the basis for efficient predictive tools based on computations that would enable high-throughput screening of the similar materials. For validation, Eu:Al₂O₃ ceramics were synthesized by gelcasting techniques and vacuum sintering method with photoluminescence properties and decay time characterized here.

2. Method

2.1 Density functional theory simulations with U correction (DFT + U)

The ab initio simulations were performed with VASP, a plane wave DFT package [18]. PBE exchange and correlation functional was used with the plane wave cutoff set to 500 eV. To properly describe the f-electrons of Eu ions, we applied the DFT + U method with an effective U value of 6 eV, according to several previous simulation studies of Eu-containing compounds [19–21]. We paid particular attention to the issues of unphysical sub-orbital occupations raised in recent DFT + U studies, which can lead to incorrect energetics and ionic structures in some materials [22–25]. With a simple scheme proposed recently, which involves ramping the U value iteratively during ionic relaxation [24, 25], we did not find sub-orbital occupations significantly more stable than the ones obtained by the standard method for the systems studied here, although more thorough investigation might be needed.

The target doping concentration of synthesized Eu:Al₂O₃ is 0.1 at. % is well below the dilute solution limit. For example, the probability of a Eu substitution have no other Eu substitution in a nearest neighbor configuration, i.e., all three nearest cation sites around the Eu are occupied by Al ions, is (99.9%)³ = 99.7% in a random distribution. Similarly, in the case of Eu²⁺ compensated with oxygen vacancy, the probability of a Eu dopant in the α-Al₂O₃ lattice (assuming six coordinated, see detailed discussions below) does not have neighboring oxygen vacancy is 99.8%. Therefore, it is necessary to consider the defects as isolated. We note, however, our simulations indeed found considerable association between certain defects, especially in the case of Eu²⁺ and oxygen vacancy (binding energy of 2.5 eV in a 3 × 3 × 1 supercell). Such association would inevitably begin to manifest when the doping concentration increases, and should be taken into consideration in heavily doped cases.

Within the plane wave DFT frame, the periodic system containing isolated defects must be dealt with care. Especially, charged defects, which are neutralized with electron jellium in the present study, can considerably slow the convergence against system size [26]. To resolve this issue, we adopted a correction scheme proposed by Hine et al [27]. In this scheme, a series of supercells of different sizes and shapes containing the same defect are simulated, and the corrected energy is obtained by extrapolating a linear relationship between the energy and the Madelung potential of each supercell (calculated as a function of the defect charge and cell geometry) to infinite system size. For each charged defect in the present study, we fully relaxed four hexagonal corundum supercells (2 × 2 × 1, 2 × 2 × 2, 3 × 3 × 1, 2 × 2 × 3) to extrapolate the corrected defect energy. For Eu³⁺ substitution, no addition charge is involved and the results from 3 × 3 × 1 supercell (270 atoms) are used. For all the structures, relaxation was conducted until forces on all the atoms are below 0.01 eV/Å.

2.2 Synthesis and characterization of Eu: Al₂O₃

0.1 at. % Eu: Al₂O₃ were synthesized by gelcasting technique. Vacuum sintering method were adopted here to provide a cost-effective route to manipulate the valence state of Eu in Eu:Al₂O₃. Eu was introduced in the form of Eu₂O₃ (99.5%, Sigma-Aldrich) and high-purity α-Al₂O₃ powder (>99%) (CR-10, Baikowski, Annecy, France, D₅₀ = 0.45 μm) was used as the matrix material. After drying and de-binding of gelled Eu:Al₂O₃, the material is sintered in a vacuum furnace (10⁻³-10⁻⁴ Pa) at the temperature 1400-1850 °C for 8 hours with the final sample diameter around 3 mm and thickness in the range of 3-5 mm.

After sintering, the room temperature photoluminescence emission and excitation spectra of Eu: Al₂O₃ were recorded in an apparatus consisting of a Xenon lamp, two grating monochromators and a synchronous light detection system (Fluorolog-Tau-3, Jobin Yvon Inc. Horiba, Japan). The measurements were performed with internal corrections and compensation for the light source. Decay curves were also recorded using a pulsed Nd:YAG laser at 266 nm or 355 nm (Spectron Laser System SL802G, Rugby, UK) with a pulse energy of approximately 5 mJ, 10 Hz repetition rate and 5 ns duration.

3. Results and discussion

3. 1 Density functional theory simulations with U correction (DFT + U) of Eu²⁺/Eu³⁺:α-Al₂O₃

We first investigated the defect mechanism for Eu doping in α-Al₂O₃. Mössbauer measurement has indicated that the Eu³⁺ dopant in α-Al₂O₃ has a coordination number of six [28]. There have also been previous work hypothesizing that the Eu³⁺ dopant would substitute Al³⁺, rather than occupy interstitial sites, based on the bonding covalency and similar X-ray diffraction pattern between pure and doped alumina [28, 29]. In this study, we examined both substitution and interstitial mechanisms. The preferred one was found to be the substitution of Al³⁺ by Eu³⁺ as described by the following defect reaction in Eq. (1):

This should come as no surprise even though both Al³⁺ substitution and octahedral interstitial (tetrahedral interstitial site is too small for large ion such as Eu³⁺) provide the same coordination environment for Eu³⁺. The interstitial mechanism places Eu³⁺ adjacent to Al³⁺ ions, causing strong lattice distortions. It also needs to be charge compensated by O^2- interstitials or Al³⁺ vacancies, incurring large energetic penalties.

Interestingly, Eu²⁺ dopant also prefers a similar substitution mechanism, even though both substitution and interstitial require other defects (considering the most likely mechanisms: one O^2- vacancy per two Eu²⁺ substitutions versus one O^2- interstitial per one Eu²⁺ interstitial). The defect reaction equation, describing the reduction of Eu³⁺ to Eu²⁺ in Al₂O₃ host lattice, can therefore be written as Eq. (2):

It is worth noting that both isolated Eu³⁺ and Eu²⁺ substations have six-coordinated environments. For both cases, the first coordination shell is well-defined and similar to that of Al³⁺ in Al₂O₃, with two sets of Eu-O bond lengths. It can be seen that, in spite of the substantial size difference between europium and aluminum ions, isolated Eu dopant can be constricted by the host lattice and assume the environment of host cations, at least at a low dopant concentration. This can also apply to other host materials for selecting desired local environment for the luminescence dopant.

As both Eu³⁺ and Eu²⁺ would assume the same lattice site, the reduction reaction of Eu³⁺ to Eu²⁺ can be written as the following Eq. (3), by combining Eq. (1) and (2):

The reduction enthalpy for this reaction can then be calculated in Eq. (4):

where $(E_{2E{u}^{2+}}-E_{2E{u}^{3+}})$ is the difference in lattice energy between Eu²⁺ and Eu³⁺ doped structures, and ${\mu }_O\left(T,P\right)$ is calculated as:

where $E_{O_2}$ is the energy of O₂ molecule at 0K, which was calculated from DFT by placing an isolated O₂ molecule in the simulation box. The standard chemical potential of oxygen at higher temperatures can be calculated by correcting $E_{O_2}$ with $\text{Δ}{\mu }_O^{\text{Ο}}(T)$, which is obtained from thermodynamic tables [30]. The DFT + U simulations calculated the value of ($E_{2E{u}^{2+}}+E_{V_O^{\mathrm{..}}}+\frac{1}{2}{E}_{O_2}-E_{2E{u}^{3+}}$) as 3.50 eV. Using this value, the reduction level can be estimated as a function of oxygen partial pressure according to reaction kinetics theory. Ignoring the vibrational entropy contribution, the temperature-dependence equilibrium constant follows the Boltzmann distribution:

where $\left[E{u}_{Eu}^{\text{'}}\right]$, $\left[E{u}_{Eu}^{\times }\right]$, $\left[V_O^{\mathrm{..}}\right]$, $\left[O_O^{\times }\right]$ are equilibrium concentrations of Eu²⁺, Eu³⁺, oxygen vacancies, and oxygen ions, respectively, and they satisfy:

and, considering that $\left[V_O^{\mathrm{..}}\right]+\left[O_O^{\times }\right]$ gives the total concentration of oxygen sites in the host Al₂O₃:

where c_Eu is the doping concentration of Eu. Solving Eqs. (6), (7) and (8), the Eu²⁺ concentration can be obtained. The results are plotted in Fig. 1. The Eu²⁺ concentration shows a dependence on oxygen partial pressure with a characteristic exponent of −1/6. At high oxygen partial pressure, reduction is limited. Typical vacuum furnaces for high temperature sintering can maintain oxygen partial pressure in the range of 0.21 × (10⁻³-10⁻⁴) Pa, which is marked with the dotted lines. It can be seen that, for p(O₂) in this range, a high temperature above 1700℃ can reduce majority (>95%) of the Eu³⁺ to Eu²⁺. Such a high temperature can also encourage oxygen diffusion so that the reduction equilibrium can be reached efficiently.

 

Fig. 1 Calculated Eu²⁺ concentration (in log₁₀(c), where c = [Eu²⁺]/[Eu]) versus oxygen partial pressure (in log₁₀(P_O), where P_O is oxygen partial pressure in Pa) in the temperature range between 1400~1900 °C. Vertical dashed lines mark the range of oxygen partial pressure used in vacuum synthesize. The horizontal dashed line indicates c = 95%.

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The electronic band structures of Eu³⁺ and Eu²⁺ doped α-Al₂O₃ are also calculated from the DFT + U simulations, as shown in Fig. 2. We observe no substantial differences between the electronic bands contributed by the host material, α-Al₂O₃ between the two cases. The defect states contributed by the dopants in the band gap are well defined, and show no obvious characteristics of the α-Al₂O₃ symmetry. Therefore, we expect the luminescence in both cases to retain its characteristic spectrum. However, it is worth noting that the effect of oxygen vacancy, especially the association between the dopant and vacancy, is not considered here. This could potentially cause alterations of the spectrum of the Eu²⁺ doped material, which warrants further investigations.

 

Fig. 2 Band structure of Eu³⁺ (a) and Eu²⁺ (b) doped alumina. The Fermi energy is set to 0 eV. For comparison, the two plots are arranged so that the energy levels contributed mainly by alumina are aligned. For clarity, unoccupied and occupied bands are shown in blue. Spin up and spin down levels are plotted with solid and dotted lines, respectively.

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3.2 Photoluminescence characterization of Eu²⁺/Eu³⁺:Al₂O₃

3.2.1 Room temperature photoluminescence emission and excitation of Eu²⁺/Eu³⁺:Al₂O₃

Room temperature photoluminescence excitation and emission spectra of Eu: Al₂O₃ were recorded in Fig. 3 and Fig. 4. The photoluminescence excitation spectrum of Eu²⁺: Al₂O₃ (Fig. 3) shows two over-lapped excitation peaks with the centers at 277 nm and 330 nm, coming from the emission behavior of Eu²⁺. The blue emission of Eu:Al₂O₃ comes from the transition of Eu²⁺ between 4f⁶5d¹ and 4f⁷ (⁸S_7/2) ($E{u}^{2+}(4f^7)+h\nu \to E{u}^{2+*}(4f^{6}5d^1)$). Such f-d transition and broadband emission are usually strongly dependent on the local atomic environment of the activation center. Gaussian fitting analysis of the excitation spectrum of vacuum-sintered Eu²⁺: Al₂O₃ (monitored at 430 nm, Fig. 3) showed two broad excitation peaks at 277 nm and 330 nm, respectively, indicating that the Eu²⁺ ions are located in low-symmetry sites with a broad crystal field distribution [31] and a large field splitting of 5d band [29]. Such excitation spectrum is different from those measured for Eu²⁺:Al₂O₃ powder [29] and Eu²⁺:Al₂O₃ film [32]. It is possible that the fabrication process has led to changes in the local symmetry of the Eu²⁺ activator. As shown by the DFT + U calculations, the Eu²⁺ dopants substitute Al³⁺, accompanied by oxygen vacancies. The oxygen vacancies may form F⁺-centers [33], and contribute to broad excitation and emission spectra in the UV region. Additionally, strong association may exist between dopants and vacancies. Under favorable synthesis conditions, e.g. slow cooling rate, defect clusters such as $Eu{(2+)}_{Al}^{\text{'}}-V_O^{\mathrm{..}}$ may be obtained, which leads to a change in the local symmetry of the Eu²⁺ activator and, consequently, the crystal field felt by Eu²⁺ ions. Indeed, the bulk samples may experience slower cooling in the center than powders and films even when the same nominal cooling rate is used [34]. Other factors, such as phase separation, defect segregation at grain boundary, etc., could also contribute to the changes in the local atomic environment of the activation centers, which warrants further investigations.

 

Fig. 3 Room temperature photoluminescence excitation spectra of vacuum-sintered 0.1at% Eu²⁺: Al₂O₃ monitored at 430 nm with corresponding Gaussian fitting curves.

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Fig. 4 Room temperature photoluminescence emission spectra of vacuum-sintered 0.1at% Eu²⁺: Al₂O₃ and air-sintered 0.1at% Eu³⁺: Al₂O₃ excited with 277 nm and 330 nm (dark line: Eu²⁺:Al₂O₃; red line: Eu³⁺:Al₂O₃).

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Air-sintered Eu:Al₂O₃ was also examined under excitation by UV light (277 nm), which showed the characteristic photoluminescence peaks of Eu³⁺ at 588 nm (⁵D₀-⁷F₁) and 611 nm (⁵D₀-⁷F₂) [35–37]. In comparison, under excitation with UV light (277 nm and 330 nm), vacuum sintered Eu:Al₂O₃ only showed one broad peak in the wavelength range of 330-600 nm with a peak center near 430 nm but none of the characteristic peaks of Eu³⁺_. This indicates that the reduction of Eu³⁺ —› Eu²⁺ in the Al₂O₃ host was achieved by vacuum sintering at temperatures of 1750-1850 °C, as predicted by the DFT + U calculations.

3.2.2 Room temperature photoluminescence emission spectra of Eu: Al₂O₃ sintered at varying vacuum-sintering temperature

To further validate the DFT + U calculations, samples were vacuum sintered at different temperatures using the same procedure. The measured emission spectra were shown in Fig. 5. As expected, the intensity of the characteristic Eu³⁺ photoluminescence peak at 611 nm (⁵D₀-⁷F₂) decreases with increasing vacuum sintering temperature. In comparison, the emission intensity of Eu²⁺ in the blue light region increases with higher vacuum sintering temperature. The presence of Eu³⁺ is evident at and below 1700 °C, suggesting the calculated Eu²⁺ concentration may be overestimated, which requires further quantification. Nonetheless, the DFT + U calculations provided adequate guidance for selecting the correct sintering condition. It should also be noted that, low porosity and good sintering quality in the samples, a prerequisite for optical applications that require high transmittance, have been obtained at temperatures above 1700 °C.

 

Fig. 5 Photoluminescence spectra of vacuum-sintered 0.1at% Eu²⁺: Al₂O₃ at room temperature excited with 277 nm as a function of vacuum sintering temperature (normalized to the same height at the spectra maxima).

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3.2.3 Luminescence decay properties of Eu²⁺:Al₂O₃

The luminescence decay curve of the vacuum sintered (1750°C-1850°C) 0.1 at. % Eu²⁺:Al₂O₃ measured at room temperature is shown in Fig. 6, monitored at 490 nm with an excitation wavelength of 266 nm. The luminescence decay curves were fitted by double exponentials (I = A₁* exp (-t₁/τ₂) + A₂* exp (-t₂/τ₂)) with the equation parameter shown in Fig. 6. The decay time of the Eu²⁺ d-f transition is on the order of microseconds. The average decay time of the Eu²⁺ in Al₂O₃ after vacuum-sintering was calculated from the fitting process to be approximately 0.080 ms.

 

Fig. 6 Decay curve of 0.1at% Eu²⁺: Al₂O₃ (sintering temperature: 1750°C-1850°C) monitored at 490 nm with the excitation 266 nm at room temperature.

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4. Summary

Overall, it can be seen that ab-initio calculations employing an improved DFT + U method for rare earth elements successfully guided the fabrication of Eu in α-Al₂O₃ host. The simulation results showed that Eu²⁺:Al₂O₃ can be fabricated by gelcasting and a subsequent vacuum sintering process under a vacuum atmosphere of 10⁻³-10⁻⁴ Pa in the temperature region of 1750°C-1850 °C. The resultant materials show strong photoluminescence behavior with an average lifetime of 0.080 ms. Additionally, the DFT + U calculations also provided details regarding the lattice distortions and defect associations. The presented method can be easily applied to other rare earth dopants and other host materials.