Open Access
Add to BibSonomy
Abstract
Ho3+-doped low-hydroxyl (OH-) ZnF2 based fluoride glasses were prepared by using the conventional melt-quenching method in a glove box. The glasses have a composition of ZnF2-BaF2-SrF2-YF3-HoF3 (ZBSY-H), and the absorption coefficient of OH- in the ZBSY-H glasses was calculated to be only ∼0.003 cm−1 at 2.86 µm. Under the excitation of an 1120 nm laser, efficient 2.86 µm emissions were observed in the ZBSY-H glasses. The emission cross section of the ZBSY-H glasses was also calculated, and the corresponding value was ∼7.19 × 10−21 cm2. These results indicated that the ZBSY-H glasses were potential candidate for 2.86 µm laser applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, rare earth (RE) ions doped glasses have attracted much attention for their potential applications in mid-infrared (MIR) lasers and sensors [1–6]. Researchers have developed ways such as exploiting low phonon energy matrixes and increasing RE ions doping concentrations to increase the MIR emission efficiencies [7,8]. Among optical glasses, chalcogenide glasses have the lowest phonon energies (150–450 cm−1), and have been considered as ideal matrix of RE ions for highly efficient MIR emissions [9,10]. Currently, RE doped chalcogenide glasses have been used as MIR gas sensors [11]. For high RE ions doping conditions, cross relaxation processes between RE ions that can deplete the lower energy level of MIR lasers would become more efficient, which might be benefit for obtaining efficient MIR lasers [7]. While the realized RE doping concentrations in chalcogenide glasses were in a relative low level and the RE ions were easily clustering in chalcogenide glasses [8,12], which limited their applications for MIR laser [13]. Compared to chalcogenide glasses, fluoride glasses have a little higher phonon energies (420–650 cm−1) and much higher RE ions solubility (up to 1.5×105 ppm by weight) [7,14,15]. In the fluoride glass family, fluoroaluminate glasses had the highest phonon energy (∼650 cm−1) but relative good chemical stability and high glass transition temperature [16]. By using the Ho3+-doped fluoroaluminate glass fibers as the gain media, we have already obtained ∼2.9 µm fiber laser [17]. It was worth to mention that extensive previous research had focused on fluorozirconate glasses, which have been successfully used for obtaining efficient MIR lasers [18]. Other glass compositions of interest are fluoroindate glasses, they are characterized by transmittance further into the IR region and significantly lower non-radiative decay rates in comparison to fluorozirconate glasses due to their low maximum phonon energy of ∼510 cm−1. By using heavily Er3+ or Ho3+ ions doped ZrF4 or InF3 based glasses as gain media, ∼3 and 4 µm lasers have been reported by several research groups [19,20]. Despite these impressive progresses in this field, it is still necessary to explore new glass materials for MIR laser.
ZnF2 based glasses are another fluoride glass with lower phonon energies than the above AlF3, ZrF4 and InF3 based glasses [21]. RE ions doped ZnF2 based glasses have showed higher visible and near-infrared emission efficiencies than that obtained in ZrF4 based glasses [22], which made the ZnF2 based glasses could be potential gain media for highly efficient lasers. While the MIR emission properties of RE ions doped ZnF2 based glasses were rarely investigated.
In this paper, we prepared a series of Ho3+-doped ZnF2-BaF2-SrF2-YF3 (ZBSY-H) glasses by using conventional melt-quenching method in a glove box. Under an 1120 nm laser excitation, intense 2.86 µm emissions were observed in the ZBSY-H glasses. The effect of Ho3+ doping concentrations on the 2.86 µm emission intensities was investigated. In addition, a comparison study on the 2.86 µm emission properties between ZBSY-H and the other fluoride (including AlF3, ZrF4 and InF3 based) glasses was also carried out.
2. Experiments
In our experiments, all the glasses were prepared from raw materials with a high purity of 99.99%. The ZnF2 based glasses have a composition of 60ZnF2-15BaF2-10SrF2-(15-x)YF3-xHoF3 (x=0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) named as ZBSY-xH, respectively. The Ho3+ (ionic radius: ∼0.0894 nm) doping would mainly replace the position of Y3+ (ionic radius: ∼0.0893 nm) for a similar ionic radius and valence state. The AlF3, ZrF4 and InF3 based glasses have compositions of 30AlF3-15BaF2-15YF3-10MgF2-25PbF2-5HoF3, 26InF3-15ZnF2-18BaF2-8SrF2-11GaF3-12PbF2-5LiF-5HoF3, 50ZrF4-33BaF2-7AlF3-5YF3-5HoF3, named as HoAlG, HoZrG and HoInG, respectively. Firstly, 20 g well mixed batches were melted in a platinum crucible at 950 °C for 2 h. Then the samples were annealed in a copper mold around their glass transition temperatures for 5 h. All the above glasses were prepared in a glove box filled with dry nitrogen gas (H2O content: < 0.1 ppm), and finally polished to a same thickness of ∼1.2 mm for optical measurements. The obtained glasses had relative high optical quality without any macroscopic microcrystals.
Note that, fluoroindate, fluorozirconate and fluoroaluminate glasses are three types of fluoride glasses with different phonon energy. For fluorozirconate glasses, ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF) glass is well-known and commercial available. However the ZBLAN glass is prone to hydrolysis, which might affect the relative emission properties of Ho3+. Compared to ZBLAN glass, fluorozirconate glasses with a composition of ZrF4-BaF2-AlF3-YF3 show much better water resistance [23], while a similar phonon energy (∼580 cm−1). Compared to the ZrF4-BaF2-AlF3-YF3 glass, the fluoroindate glass have a lower phonon energy (∼510 cm−1), and the fluoroaluminate glass have a higher phonon energy (∼630 cm−1). Considering this, in this work, we chose those fluoride glasses as the comparison to investigate the effect of phonon energies of the matrixes on the emission properties of Ho3+ ions.
The absorption/transmission spectra of the fluoride glasses were recorded with a Shimadzu UV3600 spectrometer in the range of 200∼2500 nm and a Nicolet 6700 FTIR spectrophotometer in the range of 2500∼13000 nm, respectively. The Raman spectra were measured by using a Horiba Lab RAM spectrometer. The emission spectra in the range of 1800∼3100 nm were measured by using a grating spectrometer equipped with an InSb detector. During the measurements, the InSb detector was cooled by liquid nitrogen.
3. Results and discussions
Figure 1(a) shows the absorption spectra of ZBSY-H glasses in the spectral range of 400∼2500 nm. Absorption bands centered at 1947 nm, 1154 nm, 898 nm, 641 nm, 537 nm, 450 nm and 417 nm could be ascribed to the transitions from the ground level 5I8 to highly excited levels 5I7, 5I6, 5I5, 5F5, 5F4(5S2),5G6 and 5G5 of Ho3+ in the ZBSY-5H glasses, and the relative absorbance were 0.11, 0.06, 0.013, 0.15, 0.21, 0.26 and 0.09 for the ZBSY-5H glass, respectively. Figure 1(b) shows the infrared transmission spectrum of ZBSY-0H glass in the spectral range of 2500∼13000 nm. The infrared cutoff wavelength of ZBSY-0H glass was up to 12800 nm, which was comparable to that of a ∼2 mm thick As2S3 glass (12600 nm) [24]. The inset of Fig. 1(b) showed the enlarged transmission spectrum of the ZBSY glass in the range of 2500∼3300 nm. The absorption coefficients of residual OH- were calculated to be as low as ∼0.003 cm−1 at ∼2.86 µm by using the formula αOH=ln(Tb/T)/l, where l is the thickness of the sample and Tb, T are the transmitted intensities at the base line (∼ 3.3 µm) and at the absorption band of OH-, respectively [3]. Such low OH- content could be attributed to the dry nitrogen atmosphere in the glove box. The existence of OH- would quench the ∼2.86 µm emission of Ho3+ ions through the energy transfer between OH- and Ho3+ ions. However the relative low OH- content in the fluoride glass sample made this type of quenching have a low probability. In the future, we will try to further reduce the OH- content by optimizing the preparation processes of fluoride glasses.
Fig. 1. (a) Absorption spectra of ZBSY-H glasses in the spectral range of 400∼2500 nm. (b) Infrared transmission spectrum of ZBSY glass in the spectral range of 2500∼13000 nm. Inset: Enlarged transmission spectrum of the ZBSY glass in the range of 2500∼3300 nm.
Generally, the phonon energies of optical glasses could be obtained from the Raman spectra, and considered to be the maximum vibration frequency corresponded to the Raman peaks. Figure 2 shows the Raman spectra of the four types of undoped fluoride glasses excited by a 633 nm laser. In the Raman spectrum of the ZBSY-0H glass, there are two peaks centered at 225 cm−1 and 420 cm−1, which could be ascribed to the anti-symmetric stretching of non-bridging fluorine atoms and the Zn-F-Zn vibration, respectively [15]. So, the phonon energy of ZBSY-0H glass could be considered as ∼420 cm−1, which was lower than that of InF3 based (∼510 cm−1), ZrF4 based (∼580 cm−1) and AlF3 based (∼630 cm−1) glasses [15,25]. Basically, lower phonon energy of matrix would result in a smaller multiphonon relaxation rate for the transitions of RE ions [26], which would be also beneficial for obtaining highly efficient ∼2.86 µm emission.
Excited by an 1120 nm laser, intense emissions centered at 2030 nm and 2859 nm were observed from the ZBSY-H glasses, which were related to the 5I7→5I8 and 5I6→5I7 transitions of Ho3+ ions, respectively. Figure 3(a) shows the mid-infrared emission spectra of ZBSY-H glasses with different Ho3+ doping concentrations. When the excitation power density was fixed at 1.66 W/cm2, the 2859 nm emission intensities increased monotonously with increasing Ho3+ doping concentration from 0.5 to 5 mol%, as shown in the inset of Fig. 3(a). This could be attributed to the more effective CR process (5I7→5I8 (Ho3+): 5I7→5I5 (Ho3+)) at higher Ho3+ concentrations (shown in Fig. 3(b)) [27], which could increase the fraction of ions in level 5I6 (through the more effective multi-phonon assisted relaxation process from the level 5I5 to the level 5I6) and enhance the 2859 nm emission. With further increasing the Ho3+ doping concentration to 10 mol%, the 2859 nm emission intensities decreased gradually, which might be caused by concentration quenching effect [4]. The increase of the 2030 nm emission intensity with increasing Ho3+ doping concentration from 0.5 to 2 mol% could be ascribed to the more effective pumping. And the decrease of 2030 nm emission intensities with further increasing the Ho3+ doping concentration to 10 mol% could be mainly ascribed to the CR process (5I7→5I8 (Ho3+): 5I7→5I5 (Ho3+)) and concentration quenching effect.
Fig. 3. (a) 2 µm and 2.86 µm emission spectra of ZBSY-H glasses. Inset: Dependence of the 2.86 µm emission intensities on Ho3+ concentrations. (b) Energy level diagram and mechanism of the IR emissions of Ho3+.
To demonstrate the potential applications of ZBSY-H glasses for 2.9 µm lasers, we calculated the emission cross-section of transition 5I6→5I7 of Ho3+ in ZBSY-H glass by using Fuchtbauer-Ladenburg equation [28],
Fig. 4. Calculated stimulated emission and absorption cross sections of the transition 5I6↔5I7 of Ho3+ in ZBSY-5H glass.
In addition, we also did a comparison study on the ∼2.86 µm emission properties between ZBSY-H and HoInG, HoZrG and HoAlG glasses. Figure 5(a) showed the transmission spectra of ZBSY-5H, HoInG, HoZrG and HoAlG glasses. The infrared cut off wavelength of ZBSY-5H glass (12800 nm) was longer than that of HoInG, HoZrG and HoAlG glasses (11700, 9900, 9000 nm, respectively), this indicated that the ZBSY-5H glass might have the lowest phonon energy among the four fluoride glasses. For a fixed excitation power of 1.66 W/cm2 at 1120 nm, intense ∼2.86 µm emission could be obtained from all the four glasses. The obtained emission intensity obtained in the ZBSY-5H glass was stronger than that obtained in HoInG, HoZrG and HoAlG glasses, which was coincide with the statement that mentioned above, more efficient MIR emissions could be obtained from RE ions doped in matrixes with lower phonon energies.
Fig. 5. (a) Transmission spectra of ZBSY-5H, HoInG, HoZrG and HoAlG glasses. (b) 2.86 µm emission spectra of ZBSY-5H, HoInG, HoZrG and HoAlG glasses under the excitation of 1120 nm laser.
Furthermore, we measured the lifetimes of 5I6 energy level of HoAlG, HoZrG, HoInG and ZBSY-5H glasses by using a 450 nm nanosecond pulse laser as the pump source, as shown in Fig. 6. All the lifetimes were single exponential fit, and the values for HoAlG, HoZrG, HoInG and ZBSY-5H glasses were 1.62 ms, 2.23 ms, 2.89 ms and 3.93 ms, respectively. The lifetime of the 5I6 energy level of Ho3+ in ZBSY-5H glass was longer than that of HoAlG, HoZrG and HoInG glasses, which would be of benefit to obtain efficient 2.86 µm emission. The fluorescence quantum efficiency of ∼2.86 µm emission, which was one of the most important optical properties of glass materials, could be calculated by using the formula η=β (τmeas/τrad) [35], where β is the branch ratio of the 5I6→5I7 transition, τmeas is the measured lifetime of 5I6 energy level and τrad is the calculated radiative lifetime of 5I6 energy level of Ho3+, respectively. Based on the Judd-Ofelt theory, the τrad of the 5I6 energy level of Ho3+ in HoAlG, HoZrG, HoInG and ZBSY-5H glasses were calculated to be 4.85 ms, 5.87 ms, 5.2 ms and 4.34 ms, and the β of the 5I6→5I7 transition of Ho3+ in HoAlG, HoZrG, HoInG and ZBSY-5H glasses were 11.5%, 10.6%, 10.9% and 8.9%, respectively. Therefore, the quantum efficiencies (η) of 2.86 µm emission in HoAlG, HoZrG, HoInG and ZBSY-5H glasses were calculated to be 3.84%, 4.03%, 6.06% and 8.06%, respectively. These results indicated that the ZBSY-H glasses were potential gain media for 2.86 µm laser applications. In the future, we will design and construct appropriate laser cavities to realize highly efficient lasing at ∼2.86 µm.
4. Conclusion
In conclusion, we prepared Ho3+-doped ZBSY glasses by using conventional melt-quenching method in a glove box. The absorption coefficient of OH- in the ZBSY-H glasses was as low as 0.003 cm−1 at 2.86 µm. Under the excitation of 1120 nm laser, intense 2.86 µm emissions were observed in the ZBSY-H glass and the emission intensity was much stronger than that obtained in Ho3+-doped AlF3, ZrF4 and InF3 based glasses for a same excitation power density. The FWHM of the 2859 nm emission obtained from ZBSY-H glass was 124 nm and the peak emission cross section was calculated to be ∼7.19 × 10−21 cm2 at 2.86 µm. Our results indicated that the ZBSY-H glasses were potential gain media for MIR laser applications.
Funding
National Natural Science Foundation of China (61827821, 61527823, 11774132); Key Technology Research and Development Project of Jilin Province (20180201120GX); Major Science and Technology Tendering Project of Jilin Province (20170203012GX); Field Funding for Equipment Pre-research (61404140106); Opened fund of State Key Laboratory of Luminescence and Applications (SKLA-2019-05).
Disclosures
The authors declare no conflict of interest.
References
1. X. Wen, G. Tang, J. Wang, X. Chen, Q. Qian, and Z. Yang, “Tm3+ doped barium gallo-gernanate glass single-mode fibers for 2.0 µm laser,” Opt. Express 23(6), 7722–7731 (2015). [CrossRef]
2. Y. Guo, Y. Tian, L. Zhang, L. Hu, N. K. Chen, and J. Zhang, “Pr3+-sensitized Er3+-doped bismuthate glass for generation high inversion rates at 2.7 µm wavelength,” Opt. Lett. 37(16), 3387–3389 (2012). [CrossRef]
3. R. Wang, X. Meng, F. Yin, Y. Feng, G. Qin, and W. Qin, “Heavily erbium-doped low-hydroxyl fluorotellurite glasses for 2.7 µm laser applications,” Opt. Mater. Express 3(8), 1127–1136 (2013). [CrossRef]
4. Y. Tian, X. Jing, B. Li, P. Li, Y. Li, R. Lei, J. Zhang, and S. Xu, “Synthesis, theoretical analysis, and characterization of highly Er3+ doped fluoroaluminate-tellurite glass with 2.7 µm emission,” Opt. Mater. Express 6(10), 3274–3285 (2016). [CrossRef]
5. Y. Nishida, T. Kanamori, T. Sakamoto, Y. Ohishi, and S. Sudo, “Development of PbF2-GaF3-InF3-ZnF2-YF3-LaF3 glass for use as a 1.3 µm Pr3+-doped fiber amplifier host,” J. Non-Cryst. Solids 221(2–3), 238–244 (1997). [CrossRef]
6. L. Gomes, V. Fortin, M. Bernier, R. Vallée, S. Poulain, M. Poulain, and S. D. Jackson, “The basic spectroscopic parameters of Ho3+-doped fluoroindate glass for emission at 3.9 µm,” Opt. Mater. 60, 618–626 (2016). [CrossRef]
7. B. Srubuvasan, E. Poppe, J. Tafoya, and R. K. Jain, “High-power (400 mW) diode-pumped 2.7 µm Er:ZBLAN fibre lasers using enhanced Er-Er cross-relaxation processes,” Electron. Lett. 35(16), 1338–1340 (1999). [CrossRef]
8. A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18(25), 26704–26719 (2010). [CrossRef]
9. V. Moizan, V. Nazabal, J. Troles, P. Houizot, J. L. Adam, J. L. Doualan, R. Moncorgé, F. Smektala, G. Gadret, S. Pitois, and G. Canat, “Er3+-doped GeGaSbS glasses for mid-IR fiber laser application: synthesis and rare earth spectroscopy,” Opt. Mater. 31(1), 39–46 (2008). [CrossRef]
10. M. Zhang, A. Yang, Y. Peng, B. Zhang, H. Ren, W. Guo, Y. Yang, C. Zhai, Y. Wang, Z. Yang, and D. Tang, “Dy3+-doped Ga-Sb-S chalcogenide glasses for mid-infrared lasers,” Mater. Res. Bull. 70, 55–59 (2015). [CrossRef]
11. X. Dai, X. Liu, L. Liu, B. Zhu, and Z. Fang, “A novel image-guided FT-IR sensor using chalcogenide glass optical fibers for the detection of combustion gases,” Sens. Actuators, B 220, 414–419 (2015). [CrossRef]
12. M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy and Pr ions,” J. Non-Cryst. Solids 326–327, 301–305 (2003). [CrossRef]
13. V. S. Shiryaev, A. P. Velmuzhov, Z. Q. Tang, M. F. Churbanov, and A. B. Seddon, “Preparation of high purity glasses in the Ga-Ge-As-Se system,” Opt. Mater. 37, 18–23 (2014). [CrossRef]
14. J. Bei, T. M. Monro, A. Hemming, and H. Ebendorff-Heidepriem, “Fabrication of extruded fluoroindate optical fibers,” Opt. Mater. Express 3(3), 318–328 (2013). [CrossRef]
15. R. M. Almeida, J. C. Pereira, Y. Messaddeq, and M. A. Aegerter, “Vibrational spectra and structure of fluoroindate glasses,” J. Non-Cryst. Solids 161, 105–108 (1993). [CrossRef]
16. F. Huang, Y. Ma, W. Li, X. Liu, L. Hu, and D. Chen, “2.7 µm emission of high thermally and chemically durable glasses based on AlF3,” Sci. Rep. 4(1), 3607 (2015). [CrossRef]
17. S. Jia, Z. Jia, C. Yao, S. Wang, H. Jiang, L. Zhang, Y. Feng, G. Qin, Y. Ohishi, and W. Qin, “Ho3+ doped fluoroaluminate glass fibers for 2.9 µm lasing,” Laser Phys. 28(1), 015802 (2018). [CrossRef]
18. X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010). [CrossRef]
19. T. Sandrock, A. Diening, and G. Huber, “Laser emission of erbium-doped fluoride bulk glasses in the spectral range from 2.7 to 2.8 µm,” Opt. Lett. 24(6), 382–384 (1999). [CrossRef]
20. A. Berrou, C. Kieleck, and M. Eichhorn, “Mid-infrared lasing from Ho3+ in bulk InF3 glass,” Opt. Lett. 40(8), 1699–1701 (2015). [CrossRef]
21. M. Matecki, M. Poulain, and M. Poulain, “Verres Aux Halogenures De Cadmium: 1.- Verres Fluores,” Mater. Res. Bull. 17(10), 1275–1281 (1982). [CrossRef]
22. B. Villacampa, R. I. Merino, V. M. Orera, R. Cases, P. J. Alonso, and R. Alcalá, “Optical properties of 4f-ions in ZnF2-CdF2 doped glasses,” Mater. Sci. Forum 67–68, 527–532 (1991). [CrossRef]
23. M. Poulain, “Halide glasses,” J. Non-Cryst. Solids 56(1–3), 1–14 (1983). [CrossRef]
24. A. Galstyan, S. H. Messaddeq, I. Skripachev, T. Galstian, and Y. Messaddeq, “Role of iodine in the solubility of Tm3+ ions in As2S3 glasses,” Opt. Mater. Express 6(1), 230–243 (2016). [CrossRef]
25. H. Chen and F. Gan, “Vibrational spectra and structure of AlF3-YF3 fluoride glasses,” J. Non-Cryst. Solids 112(1–3), 90–95 (1989). [CrossRef]
26. Y. B. Shin, W. Y. Cho, and J. Heo, “Multiphonon and cross relaxation phenomena in Ge-As(or Ga)-S glasses doped with Tm3+,” J. Non-Cryst. Solids 208(1–2), 29–35 (1996). [CrossRef]
27. J. Li, L. Gomes, and S. D. Jackson, “Numerical modeling of holmium-doped fluoride fiber lasers,” IEEE J. Quantum Electron. 48(5), 596–607 (2012). [CrossRef]
28. F. Huang, Y. Guo, Y. Ma, L. Zhang, and J. Zhang, “Highly Er3+-doped ZrF4-based fluoride glasses for 2.7 µm laser materials,” Appl. Opt. 52(7), 1399–1404 (2013). [CrossRef]
29. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962). [CrossRef]
30. G. S. Ofelt, “Intensities of crystal spectral of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962). [CrossRef]
31. M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002). [CrossRef]
32. J. Zhang, Y. Lu, M. Cai, Y. Tian, F. Huang, and S. Xu, “Highly efficient 2.84-µm emission in Ho3+/Yb3+ codoped tellurite-germanate glass for mid-infrared laser materials,” IEEE Photonics Technol. Lett. 29(17), 1498–1501 (2017). [CrossRef]
33. L. Wetenkamp, G. F. West, and H. Többen, “Optical properties of rare earth-doped ZBLAN glasses,” J. Non-Cryst. Solids 140, 35–40 (1992). [CrossRef]
34. Q. Liu, Y. Tian, W. Tang, F. Huang, X. Jing, J. Zhang, and S. Xu, “Broadening and enhancing 2.7 µm emission spectra in Er/Ho co-doped oxyfluoride germane silicate glass ceramics by imparting multiple local structures to rare earth ions,” Photonics Res. 6(4), 339–345 (2018). [CrossRef]
35. F. Auzel, D. Meichenin, and H. Poignant, “Laser cross-section and quantum yield of Er3+ at 2.7 µm in a ZrF4-based fluoride glass,” Electron. Lett. 24(15), 909–910 (1988). [CrossRef]
