The Impact of BiF3 Doping on the Yb3+ to Yb2+ Reduction during the LiYF4:Yb3+ Crystal-Growth Process

Abstract

Here, we report on the opportunity to suppress Yb³⁺ to Yb²⁺ dopant-ion reduction in LiYb_xY_1−xF₄ mixed crystals during growth processes, using the Bridgmen–Stocbarger technique in graphite crucibles in vacuum. This was carried out by the additional doping of the LiF-YF₃-YbF₃ powder mixture with 1% of BiF₃ additive. The crystals of LiY_0.8Yb_0.2F₄ and LiY_0.8Yb_0.2F₄ with BiF₃ doping in the charge, were grown. The spatial distribution of the spectral-kinetic properties of Yb³⁺ and Yb²⁺ ions along the grown crystalline-boules were studied. It was established that the Yb²⁺ concentration rises during the LiY_0.8Yb_0.2F₄ crystal-growth processes without the BiF₃ additive: the absorption coefficient of Yb²⁺ (π-polarization) at 340 nm rises from 0 (at the beginning of the boule) to 2.5 cm⁻¹ (at the end of the boule). In contrast, the undetectable absorption of Yb²⁺ along the crystals grown from the BiF₃ doped melt was displayed. The luminescence-decay time of Yb³⁺ decreases from 3.7 to 1.8 ms from the beginning to the end of the LiY_0.8Yb_0.2F₄ boule grown from the BiF₃ undoped melt, and stays constant (~3.7 ms) along the samples grown with BiF₃. Here we demonstrate a positive effect of BiF₃ doping on the optical homogeneity of LiYF₄:Yb³⁺ crystals.

1. Introduction

LiYF₄ fluoride crystals doped with Yb³⁺ ions are well-known continuous-wave laser materials with room temperature tuning-ranges of 997–1065 nm and 998–1076 nm for σ and π polarizations, respectively [1]. Due to the large gain-bandwidth, the LiYF₄:Yb³⁺ crystals can be implemented as an active medium to obtain laser oscillation in a subpicosecond-pulse regime under cryogenic cooling [2]. The unique energy-level structure of Yb³⁺ ions determines the high efficiency of the optical-refrigeration effect. For example, an active medium based on LiYF₄:Yb³⁺ can reduce the temperature the of GaAs/InGaAs double-heterostructure with 2 μm thickness, down to 165 K [3].

Common problems which reduce efficiency for both laser performance [4,5,6] and laser cooling [7] is the conversion of Yb ions from a trivalent to a divalent state. Ions such as Sm³⁺ and Eu³⁺ also demonstrate the same tendency. The optical properties of Yb²⁺ ions were investigated in oxides [8], various fluorides [9,10], and fibers [5]. Due to the completed 4f electron shell of Yb²⁺, its absorption spectrum is formed by interconfigurational 4fn→4fn-1 5d transitions, corresponding to the 170–400 nm spectral range [11]. In addition, the intervalence charge transfer can be observed in Yb³⁺-Yb²⁺ mixed systems [12], which may affect the luminescent properties of Yb³⁺.

Part of the Yb³⁺ ions distributed in the host-matrix can be reduced to divalent state under specific crystal-growth conditions [13]. In the work [14], the authors identify some of these conditions, namely: (a) an absence of oxidizer, (b) the trivalent rare-earth ion must substitute the cation with the different valence, (c) a proximity of ionic radii of the trivalent activator and the divalent host-cation, and (d) an appropriate host-compound conducive to dopant valence-reduction. Generally, the LiYF₄ host-matrix does not satisfy any of these conditions and does not have sites for the divalent dopant; therefore, the divalent-ytterbium appearance should be associated with impurities or defects. However, the most urgent problem for the optically perfect fluoride-crystal-growth process is the presence of incontrollable oxides and the OH^- group containing impurities in the charge. Indeed, the water traces always exist in the growth-chamber environment [15].

A common way to deal with Yb³⁺-Yb²⁺ conversion is the conduction of crystal-growth procedures under a fluorinating atmosphere, for example, in the presence of HF or CF₄ gases [16]. As mentioned above, despite the effectiveness of this method, the use of a fluorinating atmosphere is related to notable technical difficulties. It is worth keeping in mind the fact that the additional Bi-doping procedure can improve the optical properties of rare-earth-doped aluminosilicate, borate, phosphate and germanate glasses [17]. This occurs due to the high electron-affinity of Bi³⁺ ions and the consequent effective reduction into a lower valence-state [18]. In addition, it is known that the Yb³⁺ and Bi⁺ ions being doped to the matrix as a pair mutually stabilizes their valence, which was shown in the PbF₂ matrix, where the conditions are in favor of Yb²⁺ ions formation [19]. In this study, we demonstrate the fact that the addition of BiF₃ to the LiF-YF₃-YbF₃ charge reduces the divalent-ytterbium-formation efficiency in LiYF₄:Yb^3+-solid solutions grown by Bridgeman technique in graphite crucibles in vacuum.

2. Materials and Methods

2.1. Material Synthesis

The crystals of LiY_0.8Yb_0.2F₄ were grown in graphite crucibles from the melt with and without 1% of BiF₃ additive, using the Bridgman technique. The fluorides of the Yttrium, Ytterbium and Bismuth powder-mixture was used as the charge. During the growth procedure, the pressure inside the crystal-growth chamber was maintained at 10⁻⁴ mbar. The melt was pulled out from the high temperature zone through a region of a thermal gradient (≈100 °C/cm). To obtain the specific optical c-axis-orientation (perpendicular to the cylinder of the boule), a seeding crystal was placed inside the crucible.

Samples were cut into a parallelepipeds with 5 × 5 × 30 mm typical dimensions. The optical axis of the crystals was perpendicular to one of the carefully polished facets.

2.2. Spectral-Kinetic Characterization of the Samples

The absorption spectra of the samples were obtained via the one-beam method, using StellarNet SL5 Deuterium/Halogen Light Source (spectral range 190–2500 nm, StellarNet, Inc. 14390 Carlson Circle Tampa, FL, USA). The experimental set-up is presented in Figure 1.

A Glan prism was used as the polarizer. Incident light (the probe beam) was focused on the sample surface using a fused-silica lens with a 5 cm focal length. Luminescence and absorption spectra were registered using the StellarNet CCD spectrometer (optical resolution up to 0.5 nm, StellarNet, Inc. 14390 Carlson Circle Tampa, FL, USA). The relative accuracy of the light-intensity measurements was approximately 0.5%. Luminescence excitation was carried out using pulse-periodic radiation of the InAlGaAs laser diode ATC-C1000-100 (FWHM 3 nm, “Semiconductor devices” LLC, Moscow, Russia) operating at 935 nm wavelength. Excitation laser-pulse duration and pulse repetition rate were 5 ms and 10 Hz, respectively. Luminescence-decay curves were detected using the monochromator DMR-4 (OPTICS LLS, Moscow, Russia), the photomultiplier FEU-62 (ZAPADPRIBOR LLC, Moscow, Russia, 400–1200 nm operating spectral range), and the Bordo 211 digital oscillograph (AURIS LLC, Moscow, 10 bit and 200 MHz bandwidth).

3. Results and Discussion

Absorption and Luminescence Spectrum of LiY_0.8Yb_0.2F₄ and LiY_0.8Yb_0.2F₄:BiF₃ (1%)

Spin-orbit interaction splits the ²F term of the Yb³⁺ ion into two ²F_5/2 and ²F_7/2 manifolds, where ²F_7/2 is the ground state. These manifolds split into three and four Stark sub-levels_, respectively. The polarized absorption spectra of the crystals are shown in Figure 2.

Each infra-red spectrum represents six absorption bands, due to the selection rules for each polarization [20]. These results are in agreement with an already published paper [21]. Four absorption peaks in the ultraviolet spectral-range can be distinguished at 248 nm, 262 nm, 307 nm, and 347 nm. These absorption bands are also in good agreement with the M. Kaczmarek et al. paper [22], in which the Yb²⁺ impurity centers in LiYF₄ crystals were induced by X-ray radiation. In our study, Yb²⁺ centers can appear in LiYF₄:Yb³⁺ crystals during the growth process because the vacuum and the contact of the melt with the graphite crucible are the reducing conditions. In addition, the absorption spectra change significantly in different parts of the crystal boule. It can be seen from Figure 2, that the absorption bands in the UV range are more intense for the part corresponding to the end of the crystallization process, whereas the bands are almost not pronounced at the beginning of crystallization. The nonpolarized normalized-luminescence-spectra of the LiY_0.8Yb_0.2 and LiY_0.8Yb_0.2 with BiF₃ additives (1 at. % in the charge) samples under 934 nm laser-excitation, are represented in Figure 3.

The BiF₃ additive does not change the luminescence spectra of the Yb³⁺ ions in the samples, but affects the fluorescence-kinetic properties. The drastic shortening of the luminescence-decay time of the Yb³⁺ ions along the crystalline boule (with growth time) is observed for the samples without the BiF₃ additive in the charge (Figure 4). In contrast, the Yb³⁺ life-time was constant for any part of the sample grown from the BiF_3-doped charge.

Due to the simultaneous increase in absorption in the ultraviolet spectral-range and the shortening of the Yb³⁺ luminescence-decay time, it can be assumed that there are energy-transfer processes between Yb²⁺ and Yb³⁺ ions in LiYF₄:Yb³⁺ single crystals. This can be associated with the well-known fact that Yb³⁺ and Yb²⁺ ions can form complex charge-transfer states [23]. The origin and the real mechanism of the interaction require further investigation.

It is important to note that the presence of Bi ions in the samples does not manifest itself in the optical spectra. There are two reasons for this: (1) the bismuth in any valence state is absent or the concentration is too low in the samples, due to the volatility of the Bi-components; (2) the Bi has a valence state in the grown crystal which cannot be detected in the visible and near-IR spectral-ranges. That is why we have studied the impact of the BiF₃ doping effect on the spectroscopic properties of Yb³⁺ and Yb²⁺ ions along the crystalline boule.

The dopant concentration is proportional to the absorption coefficient, and their distribution can be described by the Gulliver–Pfann law [24]:

(1)$C\left(g\left(z\right)\right)=C_0\ast k_{eff}\ast {\left(1-g\left(z\right)\right)}^{k_{eff}-1},$

where k_eff is the effective dopant-segregation coefficient, g(z) identifies the specific part of the crystal which can be expressed as: g(z) = z/L, where L is the total length of the sample and z is the distance from the beginning of crystallization.

Figure 5 shows the dependencies of the polarized absorption-coefficient at 340 nm of the LiY_0.8Yb_0.2F₄ crystal samples grown from the melt, with and without 1%of BiF₃ additive along the direction of growth, where z = 0 corresponds to the beginning of sample crystallization. The sample of crystal grown from the BiF₃-doped melt demonstrates no detectable absorption in the ultraviolet spectral-range at any part of the crystal boule.

The distribution coefficient of Yb³⁺ ions in the LiYF₄ crystals should be close to 0.96, due to the isomorphic substitution of Y³⁺ by the Yb³⁺ ions [25]. In our LiY_0.8Yb_0.2F₄ sample, we observed the decrease in Yb³⁺ concentration with a simultaneous increase in ultraviolet absorption (Figure 6) along the boule, from the beginning of crystallization to the end.

This relation between trivalent- and divalent-ytterbium absorption-coefficients is the indirect evidence of reduction processes occurring during crystal growth. Several studies devoted to the investigation of Yb²⁺ distribution along fluoride crystals found that the segregation coefficient of Yb²⁺ in YbF₃:CaF₂ crystals varies from 0.68 to 0.74, depending on Yb concentration [26]. In YbF₃:BaF_2, the segregation coefficient of divalent ytterbium equals 0.59 [24]. The implementation of formula (1) on the dependencies in Figure 6 gives the effective-distribution-coefficient values 0.98 and −0.7 for Yb³⁺ and Yb²⁺, respectively. Because k_eff must be positive, the Yb²⁺ ion content distribution along the crystal boule cannot be described by the Gulliver–Pfann equation. It can probably be explained by the high volatility of the bismuth salts and LiBiF₄ compound. It means that the chemical composition of the melt and the crystallization conditions are drastically changed with the time of the crystal-growth process, which contradicts the basic assumptions in the derivation of the Galiver–Pfann law.

In addition, it has to be taken into account that, besides the significant rise in ultraviolet absorption, there is a drastic shortening of the luminescence-decay time of the Yb³⁺ ions along the crystal without Bi doping, which is not evident for the LiY_0.8Yb_0.2F₄:BiF₃ (1%) sample (Figure 7).

The origin and the exact mechanism of the interaction require further investigation. It is known that Yb³⁺ and Yb²⁺ ions can form complex charge-transfer states [23]. It can be assumed that the BiF₃ additive sufficiently improves the optical quality of the LiYF₄:Yb³⁺ materials, which were grown using the Bridgman technique in above-mentioned conditions. Finally, it was observed, that the addition of the BiF₃ additive to the charge sufficiently improves the optical quality of the LiYF₄:Yb³⁺ materials, which were grown using the Bridgman technique in above-mentioned conditions.

It is also important to note that Bi doping cannot be the universal solution for the Yb³⁺-Yb²⁺ conversion problem, due to the near-infrared absorption of the low-valence Bi ions, therefore disturbing the original spectrum of the samples. In addition, the crystallization temperature must be higher than the volatilization temperature of the BiF₃. This fact imposes some limitations on the crystals.

4. Conclusions

For the first time, the distribution of Yb²⁺ ions in LiYF₄:Yb³⁺ crystals was investigated. It was suggested that the formation of Yb²⁺ ions in the crystals occurs due to the growth conditions (for example, the presence of a trace quantity of water and/or synthesis in vacuum and graphite crucibles and heaters). The relation between Yb²⁺ concentration and luminescence-decay time of Yb³⁺ ions appeared to be clear and consistent. In particular, a significant increase in the Yb²⁺ absorption coefficient occurs simultaneously with Yb³⁺ luminescence quenching. The addition of BiF₃ to the melt led to the absence of the UV absorption bands corresponding to the Yb²⁺ ions. In its turn, Yb³⁺ luminescence-decay time remains stable for different parts of the crystals. The mechanism of energy transfer between Yb²⁺ and Yb³⁺ ions in heavily doped LiYF₄ crystals needs further investigation, because it can lower the effectiveness of the up-conversion excitation in co-doped LiYF₄:Yb:Tm/Ho/Eu laser crystals.

A positive effect of BiF₃ doping of the melt on the optical homogeneity of LiYF₄:Yb³⁺ crystals has at least been detected.

We believe that one of the main advantages of the present work is that the work reveals some useful details concerning the BiF₃-based LiYF₄:Yb³⁺ crystal growth. Indeed, the use of BiF₃ during the crystal-growth process seems to be beneficial compared to the alternative ways, such as the use of aggressive and toxic fluorinated-gases. In particular, in order to reduce the concentration of Yb²⁺ in the iYF₄:Yb³⁺ crystal, it is enough to add 17 mg of BiF₃ to the starting material to obtain 1 kg of LiYF₄:Yb³⁺ crystals. In its turn, BiF₃ powder is relatively cheap, compared to fluorinated gases. The addition of BiF₃ powder allows the exclusion of several steps in the technology of the crystal-growth process. In particular, it allows for reducing the time of the drying of the starting material from a range of 12 to 20 h, to 2 to 4 h. In addition, the use of BiF₃ allows for the performance of the preparatory pumping of the vacuum chamber up to 10⁻¹–10⁻² Pa, compared to 10⁻⁴–10⁻⁵ Pa (without BiF₃). It reduces the time of crystal growth or lowers the requirements imposed on the vacuum-pump system.

Author Contributions

Conceptualization, A.K., S.K., O.M., A.N., V.S. and A.K.; formal analysis, M.P., M.G. and A.N.; investigation, A.K., N.A., S.K., O.M., A.N., V.S. and A.K.; resources, M.P., M.G. and A.N.; writing—original draft preparation, A.N., A.K.; writing—review and editing, A.N., V.S., M.P. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures

Figure 1. The experimental setup for registration of the absorption spectrum of the samples. (1) broadband StellarNet halogen and deuterium light-source; (2) Glan–Taylor prism; (3) the sample; (4) CCD StellarNet spectrometer. The samples were moved along the z-axis that is perpendicular to the probe beam.

Figure 2. Polarized absorption spectra of two different parts of the LiY0.8Yb0.2F4 and LiY0.8Yb0.2F4:BiF3 (1%) crystals (a,c)—the beginning of crystallization, (b,d)—the end of crystallization.

Figure 3. The normalized luminescence-spectra of the LiY0.8Yb0.2 and LiY0.8Yb0.2:BiF3 (1%) samples under 934 nm laser-excitation.

Figure 4. Luminescence-decay time of Yb3+ (1020 nm) under 934 nm excitation along the crystals (along z-axis).

Figure 5. Absorption coefficient at 340 nm along theLiY0.8Yb0.2F4 crystals grown from the melt, with and without 1% of BiF3 additive for π (a) and σ (b) polarizations.

Figure 6. Yb3+ and Yb2+ absorption-coefficient along the LiY0.8Yb0.2F4 crystal.

Figure 7. (a) Yb3+ and (b) Yb2+ absorption along the LiY0.8Yb0.2F4 crystal in ln(α) vs. ln(1−z/L) coordinates, where α is the absorption coefficient, z represents the beginning of the sample crystallization, and L is the full length of the sample.

References

1. Alderighi, D.; Pirri, A.; Toci, G.; Vannini, M. Tunability enhancement of Yb:YLF based laser. Opt. Express; 2010; 18, pp. 2236-2241. [DOI: https://dx.doi.org/10.1364/OE.18.002236] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/20174052]

2. Kawanaka, J.; Yamakawa, K. 30-mJ, diode-pumped, chirped-pulse Yb:YLF regenerative amplifier. Opt. Lett.; 2003; 28, pp. 2121-2123. [DOI: https://dx.doi.org/10.1364/OL.28.002121] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/14587835]

3. Seletskiy, D.V.; Melgaard, S.D.; Epstein, R.I.; Di Lieto, A.; Tonelli, M.; Sheik-Bahae, M. Local laser cooling of Yb:YLF to 110 K. Opt. Express; 2011; 19, pp. 18229-18236. [DOI: https://dx.doi.org/10.1364/OE.19.018229] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/21935189]

4. Kirchhof, J.; Unger, S.; Schwuchow, A.; Jetschke, S.; Reichel, V.; Leich, M.; Scheffel, A. The influence of Yb2+ ions on optical properties and power stability of ytterbium-doped laser fibers. Opt. Compon. Mater. VII; 2010; 7598, 75980B.

5. Rydberg, S.; Engholm, M. Experimental evidence for the formation of divalent ytterbium in the photodarkening process of Yb-doped fiber lasers. Opt. Express; 2013; 21, pp. 6681-6688. [DOI: https://dx.doi.org/10.1364/OE.21.006681]

6. Gebavi, H.; Milanese, D.; Taccheo, S.; Mechin, D.; Monteville, A.; Freyria, F.S.; Bonelli, B.; Robin, T. Photodarkening of Infrared Irradiated Yb³⁺-Doped Alumino-Silicate Glasses: Effect on UV Absorption Bands and Fluorescence Spectra. Fibers; 2013; 1, pp. 101-109. [DOI: https://dx.doi.org/10.3390/fib1030101]

7. Knall, J.; Vigneron, P.-B.; Engholm, M.; Dragic, P.D.; Yu, N.; Ballato, J.; Bernier, M.; Digonnet, M.J.F. Laser cooling in a silica optical fiber at atmospheric pressure. Opt. Lett.; 2020; 45, pp. 1092-1095. [DOI: https://dx.doi.org/10.1364/OL.384658]

8. Solomonov, V.I.; Osipov, V.V.; Spirina, A.V. Luminescence and absorption of divalent ytterbium ion in yttrium-aluminum garnet ceramics. Opt. Spectrosc.; 2014; 117, pp. 441-446. [DOI: https://dx.doi.org/10.1134/S0030400X14030205]

9. Moine, B.; Courtois, B.; Pedrini, C. Luminescence and photoionization processes of Yb²⁺ in CaF₂, SrF₂ and BaF₂. J. Phys.; 1989; 50, pp. 2105-2119. [DOI: https://dx.doi.org/10.1051/jphys:0198900500150210500]

10. Kück, S.; Henke, M.; Rademaker, K. Crystal growth and spectroscopic investigation of Yb²⁺-doped fluoride crystals. Laser Phys.; 2001; 11, pp. 116-119.

11. Loh, E. ⁴f_n-⁴f_n-15d Spectra of rare-earth ions in crystals. Phys. Rev.; 1968; 175, pp. 533-536. [DOI: https://dx.doi.org/10.1103/PhysRev.175.533]

12. Barandiarán, Z.; Seijo, L. Intervalence charge transfer luminescence: Interplay between anomalous and 5d–4f emissions in Yb-doped fluorite-type crystals. J. Chem. Phys.; 2014; 141, 23. [DOI: https://dx.doi.org/10.1063/1.4902759] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/25527954]

13. Nicoara, I.; Stef, M.; Pruna, A. Growth of YbF3-doped CaF2 crystals and characterization of Yb³⁺/Yb²⁺ conversion. J. Cryst. Growth; 2008; 310, pp. 1470-1475. [DOI: https://dx.doi.org/10.1016/j.jcrysgro.2007.11.066]

14. Pei, Z.; Su, Q.; Zhang, J. The valence change from RE³⁺ to RE²⁺ ( RE = Eu, Sm, Yb) in SrB407: RE prepared in air and the spectral properties of RE²⁺. J. Alloys Compd.; 1993; 198, pp. 51-53. [DOI: https://dx.doi.org/10.1016/0925-8388(93)90143-B]

15. Baldochi, S.L.; Shimamura, K.; Nakano, K.; Mujilatu, N.; Fukuda, T. Ce-doped LiYF₄ growth under CF₄ atmosphere. J. Cryst. Growth; 1999; 205, pp. 537-542. [DOI: https://dx.doi.org/10.1016/S0022-0248(99)00164-5]

16. Bensalah, A.; Shimamura, K.; Sudesh, V.; Sato, H.; Ito, K.; Fukuda, T. Growth of Tm, Ho-codoped YLiF₄ and LuLiF₄ single crystals for eye- safe lasers. J. Cryst. Growth; 2001; 223, pp. 539-544. [DOI: https://dx.doi.org/10.1016/S0022-0248(01)00682-0]

17. Dai, N.; Xu, B.; Jiang, Z.; Peng, J.; Li, H.; Luan, H.; Yang, L.; Li, J. Effect of Yb³⁺ concentration on the broadband emission intensity and peak wavelength shift in Yb/Bi ions co-doped silica-based glasses. Opt. Express.; 2010; 18, pp. 18642-18648. [DOI: https://dx.doi.org/10.1364/OE.18.018642]

18. Truong, V.G.; Bigot, L.; Lerouge, A.; Douay, M.; Razdobreev, I. Study of thermal stability and luminescence quenching properties of bismuth-doped silicate glasses for fiber laser applications. Appl. Phys. Lett.; 2008; 92, pp. 90-93. [DOI: https://dx.doi.org/10.1063/1.2828035]

19. Zhang, P.; Chen, N.; Wang, R.; Huang, X.; Zhu, S.; Li, Z.; Yin, H.; Chen, Z. Charge compensation effects of Yb³⁺ on the Bi⁺: Near-infrared emission in PbF₂ crystal. Opt. Lett.; 2018; 43, pp. 2372-2375. [DOI: https://dx.doi.org/10.1364/OL.43.002372]

20. Sugiyama, A.; Katsurayama, M.; Anzai, Y.; Tsuboi, T. Spectroscopic properties of Yb doped YLF grown by a vertical Bridgman method. J. Alloys Compd.; 2006; 408, pp. 780-783. [DOI: https://dx.doi.org/10.1016/j.jallcom.2005.01.094]

21. Coluccelli, N.; Galzerano, G.; Bonelli, L.; Toncelli, A.; Di Lieto, A.; Tonelli, M.; Laporta, P. Room-temperature diode-pumped Yb³⁺-doped LiYF₄ and KYF₄ lasers. Appl. Phys. B Lasers Opt.; 2008; 92, pp. 519-523. [DOI: https://dx.doi.org/10.1007/s00340-008-3109-0]

22. Kaczmarek, S.M.; Bensalah, A.; Boulon, G. γ-Ray induced color centers in pure and Yb doped LiYF₄ and LiLuF₄ single crystals. Opt. Mater.; 2006; 28, pp. 123-128. [DOI: https://dx.doi.org/10.1016/j.optmat.2004.10.033]

23. MacKeen, C.; Bridges, F.; Kozina, M.; Mehta, A.; Reid, M.F.; Wells, J.-P.R.; Barandiarán, Z. Evidence that the anomalous emission from CaF₂:Yb²⁺ is not described by the impurity trapped exciton model. J. Phys. Chem. Lett.; 2017; 8, pp. 3313-3316. [DOI: https://dx.doi.org/10.1021/acs.jpclett.7b01103] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/28677980]

24. Nicoara, I.; Buse, G.; Bunoiu, M. Segregation coefficient of Yb³⁺ and Yb²⁺ ions in YbF₃ doped BaF₂ crystals. AIP Conf. Proc.; 2014; 1634, pp. 111-114.

25. Bensalah, A.; Guyot, Y.; Ito, M.; Brenier, A.; Sato, H.; Fukuda, T.; Boulon, G. Growth of Yb³⁺-doped YLiF₄ laser crystal by the Czochralski method. Attempt of Yb3+ energy level assignment and estimation of the laser potentiality. Opt. Mater.; 2004; 26, pp. 375-383. [DOI: https://dx.doi.org/10.1016/j.optmat.2003.09.015]

26. Nicoara, I.; Pecingina-Garjoaba, N.; Bunoiu, O. Concentration distribution of Yb²⁺ and Yb³⁺ ions in YbF₃:CaF₂ crystals. J. Cryst. Growth.; 2008; 310, pp. 1476-1481. [DOI: https://dx.doi.org/10.1016/j.jcrysgro.2007.11.024]