Low phonon energies and wideband optical windows of La₂O₃-Ga₂O₃ glasses prepared using an aerodynamic levitation technique

Abstract

xLa₂O₃-(100 − x)Ga₂O₃ binary glasses were synthesized by an aerodynamic levitation technique. The glass-forming region was found to be 20 ≤ x ≤ 57. The refractive indices were greater than 1.92 and increased linearly with increasing x. The polarizabilities of oxide ions were estimated to be 2.16–2.41 ų, indicating that the glasses were highly ionic. The glasses were transparent over a very wide range from the ultraviolet to the mid-infrared region. The widest transparent window among the oxide glasses was from 270 nm to 10 μm at x = 55. From the Raman scattering spectra, a decrease in bridging oxide ions and an increase in non-bridging oxide ions were confirmed to occur with increasing La₂O₃ content. The maximum phonon energy was found to be approximately 650 cm⁻¹, being one of the lowest among oxide glasses. These results show that La₂O₃-Ga₂O₃ binary glasses should be promising host materials for optical applications such as lenses, windows, and filters over a very wide wavelength range.

Introduction

Optical materials that are widely transparent from the ultraviolet (UV) to the infrared (IR) range are in great demand for many optical designs. In particular, UV–IR and visible–IR coaxial optical systems have been developed rapidly for multi-imaging cameras, vehicle video systems, endosomes, and biological microscopes in recent years. However, optical materials that are useful over wide wavelength ranges from the UV to the IR include fluoride crystals and glasses¹. The critical problems of such fluorides are difficulties in their mass production and their poor chemical durability; thus, their practical applications are limited. Although oxide glasses are more practical and commonly used as optical components because of their high productivities and chemical durabilities, their optical windows are usually much narrower. For instance, conventional oxide glasses such as silicate and borate glasses generally have good UV–visible transparency, but their IR cut-off wavelength reaches at most 2–3 μm due to the large phonon energies of the network formers².

Ga₂O₃-based glasses, on the other hand, possess good IR transparency in oxide glasses. Heavy metal gallate glasses, proposed by Dumbaugh in 1986, have attracted attention because of their longer IR cut-off edges of up to 8 μm³. In these glasses, however, the transparency in the UV to visible range is degraded due to strong s → p transitions in heavy metal cations such as Pb²⁺ and Bi³⁺. As for the alkali or alkali earth gallate glasses, Fukumi and Sakka investigated the structures of the most basic R₂O- or R’O-Ga₂O₃ binary glasses (R and R’ denote alkali and alkali earth ions, respectively) using Raman⁴ and XRD⁵. Additionally, Kokubo et al. revealed the glass-forming regions, the optical transmittance, and the structures of various ternary gallate glasses such as (R₂O or R’O)-Ta₂O₅-Ga₂O⁶, (R₂O or R’O)-Nb₂O₅-Ga₂O₃⁷, and (R₂O or R’O)-TiO₂-Ga₂O₃⁸. As for the rare-earth gallate system, however, there has only been report by Yajima et al., which described the glass formation and crystallization behaviors of 3Ln₂O₃-5Ga₂O₃ (Ln represents a rare-earth ion) compositions using an impact-quenching technique⁹. Very recently, Kidkhunthod et al. reported the glass formation of Pr₃Ga₅O₁₂ glass by a levitation technique and investigated local structure around Pr and Ga atoms¹⁰.

Levitation techniques are useful to obtain bulk glasses by vitrification of materials with high melting temperatures and low glass-forming ability, such as rare-earth gallate binary gallate systems. Levitation is a containerless melting process in which the sample is levitated and melted by non-contact heating such as laser irradiation. This enables the suppression of heterogeneous nucleation from the container wall and promotes deep undercooling and vitrification of the melt. In recent years, Al₂O₃-^{11,12,13,14,15}, TiO₂-^{16,17,18,19,20}, Nb₂O₅-^21,22,23, and WO₃-based²⁴ glasses without any network formers have been discovered using this method. These “unconventional” glasses showed outstanding dielectric, optical, and mechanical properties as a result of the specific glass compositions and structures. In this study, we aimed to obtain glasses without devitrification in the simple La₂O₃-Ga₂O₃ binary system using a levitation technique and to clarify the fundamental physical properties. In addition, Raman scattering spectra were taken for structural analysis and evaluation of phonon energies of the glasses.

Results and Discussion

Figure 1 shows the glass-forming region of the xLa₂O₃-(100 − x)Ga₂O₃ binary system on the phase equilibrium diagram²⁵. The glasses were obtained at 20 ≤ x ≤ 57. This is a slightly wider range than that of the La₂O₃-Al₂O₃ binary system: 27–50 mol% La₂O₃¹⁴. The obtained glasses (shown in the inset of Fig. 1) were colorless and transparent spheres with diameters of 2–3 mm. At x = 20, 40, and 57, however, only small-sized glasses (about 1 mm in diameter) could be synthesized, and thus we carried out thermal analysis only at these compositions. Note that ICP-MS analysis confirmed that the compositional differences between experiment and theory were less than 2 mol% for all compositions, indicating that no significant deviations in the composition occurred. Figure 2 shows the DTA curve of the 30La₂O₃-70Ga₂O₃ glass. A clear glass transition and a strong exothermic peak due to crystallization were observed. The large latent heat generated during crystallization corresponds to a large energy gap between the glassy and crystalline states. The inset of Fig. 2 summarizes the compositional dependences of the glass transition temperature T_g, the crystallization peak temperature T_p, and the temperature gap ΔT (=T_p − T_g). T_g showed a slight increase upon increasing x from 734 to 757 °C. The value of ΔT has been commonly used as a measure of glass stability. As can be seen in Fig. 2, all values of ΔT were less than 100 °C, indicating that the present glasses would be difficult to form using a conventional melt-quenching technique.

Figure 1: Illustration of the glass-forming region in the phase equilibrium diagram of the xLa₂O₃-(100 − x)Ga₂O₃ binary system²⁵ .

The inset is an image of a glass sphere.

Figure 2: DTA curve of the 30La₂O₃₋70Ga₂O₃ glass.

The inset shows the compositional dependences of the glass transition temperature T_g, the crystallization peak temperature T_p, and the temperature gap ΔT (=T_p − T_g). Closed circles, triangles, and squares represent T_g, T_p, and ΔT, respectively. Error bars (standard errors of 3 times measurements) are inside the symbol in each plot.

In most glasses, the glass-forming regions are close to the eutectic points²⁶. The eutectic points in the La₂O₃-Ga₂O₃ system, however, located at 23.1, 58.2, and 75.7 mol% La₂O₃ do not correspond to the glass-forming region, as seen in Fig. 1. This situation is similar to the Y₂O₃-Al₂O₃¹³ and Ln₂O₃-Al₂O₃ (Ln = Lu, Yb, Tm, Er, Ho, Dy, Tb, Gd, and Eu) systems¹⁴. In these systems, some equilibrium crystalline phases are absent and metastable diagrams are dominant during the cooling of the melt. In a similar way, a possible explanation for the mismatch between the glass-forming region and the phase equilibrium diagram in the La₂O₃-Ga₂O₃ system may be the absence of the LaGaO₃ phase in the metastable diagram, which is dominant in the actual devitrification process of the melt. In addition, it should be noted that ΔT took the local maximum to be at x = 25 or 55 and the local minimum to be at x = 40, as seen in Fig. 2. If only Ga₂O₃ and La₄Ga₂O₉ were the dominant phases in crystallization, there should be only one eutectic point between these two phases and ΔT should take a single maximum at that point. If some crystalline phase existed in the glass-forming region, it would reduce the glass stability or prevent vitrification at the corresponding compositions^21,27. Therefore, in the La₂O₃-Ga₂O₃ system, it would be expected that some crystalline phase exists at around x = 40, and that it forms a eutectic at around x = 25 and 55 with the Ga₂O₃ and La₄Ga₂O₉ phases, respectively. Furthermore, this crystalline phase is expected to be metastable because no stable phases were observed at this composition in the La₂O₃-Ga₂O₃ phase equilibrium diagram. A detailed investigation of metastable phases in these systems will be the subject of future investigations.

Figure 3(a) and (b) show the compositional dependences of the refractive index n_d and the density ρ in xLa₂O₃-(100 − x)Ga₂O₃ glasses, respectively. With an increase in x, n_d increased linearly from 1.921 to 1.962, and ρ increased linearly from 5.73 to 5.95 g/cm³. From the refractive index and density of the glass, the molar polarizability α_m was determined from the Lorentz–Lorenz equation.

Figure 3

(a) Refractive indices n_d, (b) densities ρ, (c) oxygen polarizabilities α_O2−, and (d) oxygen packing densities P_O2− of xLa₂O₃-(100 − x)Ga₂O₃ glasses. Error bars (standard errors of 5 times measurements in n_d and 10 times measurements in ρ) are inside the symbol in each plot.

Here, n is the refractive index, M is the average molecular weight, and N_A is Avogadro’s number. For oxides, α_m can be divided into the polarizabilities of the cations and oxide ions as follows:

where α_i is the polarizability of the cation, α_O2− is the average polarizability of the oxide ions, and N_O2− is the number of oxide ions in a molecule. Using the polarizabilities of La³⁺ (1.052 ų)²⁸ and Ga³⁺ (0.195 ų)²⁹, α_O2− values were obtained and are shown in Fig. 3(c). α_O2− linearly increased from 2.16 to 2.41 ų with increasing x. These values are rather large and correspond to those of Bi₂O₃- and TeO₂-based glasses³⁰. Therefore, La₂O₃ should have contributed to enhancing the electron density around the oxide ions and made the glass highly ionic. The average polarizabilities of cations should also increase with x because the polarizability of La³⁺ is 5 times larger than that of Ga³⁺. Nevertheless, the polarization in the La₂O₃-Ga₂O₃ binary glasses was dominated by oxide ions because the polarizabilities of cations are small compared with those of oxide ions. The oxygen packing density P_O2− of the glass was calculated from the partial molar volume of oxide ions V_O2− and the ionic radius of oxygen¹⁹. V_O2− was obtained by subtracting the contribution of cations from the molar volume V_m. Here V_m was defined as the value for the glass including 1 mol of oxide ions. The volume of 1 mol of oxide ions was calculated to be 6.92 cm³ using Shannon’s ionic radius (1.4 Å for O²⁻)³¹. Then, P_O2− was obtained by dividing V_O2− by 6.92 cm³. Figure 3(d) shows the compositional dependence of P_O2− in xLa₂O₃-(100 − x)Ga₂O₃ glasses. P_O2− decreased linearly with x from 56.6 to 51.4%. Thus, glasses with higher Ga₂O₃ content have more densely packed oxide ions.

Figure 4 shows a comparison between xLa₂O₃-(100 − x)Ga₂O₃ glasses and commercial optical glasses³² on an n_d–ν_d diagram. The refractive index n_d increased with x, whereas the Abbe number ν_d showed no significant change. Accordingly, the xLa₂O₃-(100 − x)Ga₂O₃ glasses shifted to the higher n_d region and deviated gradually from the group of commercial optical glasses as x increased. The single oscillator model of the Drude–Voigt relation shown in following equation provides an oscillator strength, f, and an inherent absorption wavelength, λ₀, which reflect the average features of the oscillators in the glass³³.

Figure 4: Comparison between xLa₂O₃-(100 − x)Ga₂O₃ glasses and commercial optical glasses³² on an n_d–ν_d diagram.

The inset shows an enlarged view. Error bars indicate the standard errors of 5 times measurements.

Here, n is the refractive index, m is the electron mass, c is the velocity of light in vacuum, e is the elementary charge, N is the number of molecules in a unit volume, f is the average oscillator strength, λ₀ is the inherent absorption wavelength, and λ is the wavelength of light. According to this relation, a plot of (n² − 1)⁻¹ versus λ⁻² is expected to be a straight line with a slope of (πmc²)/(e²Nf) and a y-axis intercept at (πmc²)/(e²Nfλ₀²). Here, N can be calculated as N = N_Aρ/M. Figure 5 shows the plots of the oscillator strength f against the inherent absorption wavelength λ₀ of La₂O₃-Ga₂O₃ glasses and other high-refractive-index glasses³³. As for the xLa₂O₃-(100 − x)Ga₂O₃ glasses, f monotonically increased from 4.38 × 10¹⁰ to 5.25 × 10¹⁰ with increasing x, whereas λ₀ remained at approximately 138 nm, showing no significant changes. Compared with other high-index glasses such as tellurite, antimonite, and heavy metal oxides, La₂O₃-Ga₂O₃ glasses are characterized by larger f and shorter λ₀. This is to say that the high refractive indices of these heavy metal oxide glasses are mainly due to the longer λ₀, and the increase in the refractive index of La₂O₃-Ga₂O₃ glasses with increasing La₂O₃ content is mainly due to the increase in f. This may be related to the fact that the absorption wavelength of La₂O₃ is much shorter than those of other heavy metal oxides such as TeO₂, Tl₂O, Sb₂O₃, PbO, and Bi₂O₃.

Figure 5: Comparison of f and λ₀ between xLa₂O₃-(100 − x)Ga₂O₃ glasses and other high refractive index glasses (tellurite, antimonite, and heavy metal oxide)³³.

Error bars (standard errors of 5 times measurements) are inside the symbol in each plot.

Figure 6(a) shows the optical transmittance spectrum of the 55La₂O₃-45Ga₂O₃ glass in the UV–visible range. There was no absorption in the visible range (400–700 nm), and the absorption edge existed at 270 nm. Because of the Fresnel loss, the maximum transmittance was approximately 80%. In general, absorption edges in the UV region are caused by electronic transitions from the valence band to the conduction band, and the cut-off wavelength is determined by the energy gap between these two bands. Thus, we evaluated the optical energy gap of the glass E_opt using the Tauc equation shown as follows.

Figure 6

(a) Optical transmittance spectrum of the 55La₂O₃-45Ga₂O₃ glass in the UV–visible region, (b) optical energy gap, E_opt, in xLa₂O₃-(100 − x)Ga₂O₃, (c) optical transmittance spectrum of the 55La₂O₃-45Ga₂O₃ glass in the IR region, and (d) absorption coefficient at 7 μm, α_7 μm, in xLa₂O₃-(100 − x)Ga₂O₃. The sample thickness was 0.71 mm in (a) and (c).

Here, α is the absorption coefficient, h is Plank’s constant, ν is the frequency of light, and A is an energy-independent constant. In addition, this equation can be rewritten as shown in following equation (5), and the optical energy gap can be determined from the discontinuity observed at a particular energy value in the d[ln(αhν)]/d(hν) versus hν plot.

The obtained E_opt values are plotted in Fig. 6(b). E_opt increased monotonically with x from 4.24 to 4.50 eV. These values are much larger than those of other glasses with refractive indices of about 1.9^34,35. Because both crystalline La₂O₃ and Ga₂O₃ have wide bandgaps of 5.8³⁶ and 4.9 eV³⁷, respectively, the large E_opt values of the La₂O₃-Ga₂O₃ glasses are convincing. In La₂O₃-Ga₂O₃ glasses, the fundamental transitions from the valence to the conduction band are expected to be O 2p → La 5d in the La–O bond and O 2p → Ga 4 s in the Ga–O bond. Considering that the energy gap in the O 2p → La 5d transition should be larger than that in the O 2p → Ga 4 s transition, the increase of E_opt in the La₂O₃-Ga₂O₃ glass is explained by the increase in the density of states of the La 5d and the O 2p orbitals with increasing x. The IR transmittance spectrum of the 55La₂O₃-45Ga₂O₃ glass is shown in Fig. 6(c). The transmittance was over 50% up until 7 μm, and the absorption cut-off wavelength reached over 10 μm. The slight absorption at approximately 3 μm is due to the OH groups in the glass. The cut-off wavelength of the 55La₂O₃-45Ga₂O₃ glass was much longer than those of typical oxide glasses such as silicate and borate², slightly longer than those of heavy metal gallate glasses (8 μm for PbO-Bi₂O₃-Ga₂O₃³ and 7.5 μm for K₂O-Ta₂O₅-Ga₂O₃ glasses⁶), and even close to those of fluoride glasses³⁸. Figure 6(d) shows the plot of α_7 μm, which represents the absorption coefficient of the xLa₂O₃-(100 − x)Ga₂O₃ glasses at 7 μm, against x. The decrease in α_7 μm indicates that the IR absorption edge shifts toward longer wavelengths with increasing La₂O₃ content.

Figure 7 shows the unpolarized Raman scattering spectra of xLa₂O₃-(100 − x)Ga₂O₃ glasses. Three distinct bands at 300, 550, and 650 cm⁻¹ were observed. The spectral shapes changed systematically with the glass compositions. With an increase in x, the band intensities at 300 and 650 cm⁻¹ increased, whereas those at 550 cm⁻¹ decreased. Detailed investigations of the Raman spectra of R₂O- or R’O-Ga₂O₃ binary glasses were carried out by Fukumi and Sakka⁴. According to them, the bands at 550 and 650 cm⁻¹ can be assigned to the stretching vibration of GaO₄ tetrahedra including non-bridging oxide ions and the bending vibration of bridging oxide ions connecting two GaO₄ tetrahedra, respectively. Furthermore, the band at 300 cm⁻¹ could be assigned to the vibration of the La–O bond³⁹. Therefore, the intensity ratio between the bands at 550 and 650 cm⁻¹ reflects the relative quantities of bridging and non-bridging oxide ions in the glass. The Raman spectra of La₂O₃-Ga₂O₃ glasses suggested that the ratio of non-bridging oxide ions increased, whereas that of bridging oxide ions decreased when La₂O₃ was substituted for Ga₂O₃. This behavior agrees with the results obtained for the R₂O- or R’O-Ga₂O₃ glasses by Fukumi and Sakka⁴. However, they also suggested that non-bridging oxide ions appeared only when the content of R₂O or R’O was higher than 43 mol%. In La₂O₃-Ga₂O₃ glasses, the intensity of the band at 650 cm⁻¹ monotonically increased with x, indicating that non-bridging oxide ions exist in the glasses at a much lower La₂O₃ content than that of R₂O- or R’O-Ga₂O₃ glasses. On the other hand, Honma et al. evaluated the roles of La₂O₃ in La₂O₃-P₂O₅ binary glasses using XPS and Raman spectroscopies²⁸. They showed that La₂O₃ acts as a network modifier, enhancing the electron density of oxide ions and increasing the ratio of non-bridging oxide ions. Similarly, in La₂O₃-Ga₂O₃ glasses, the high electron-donating ability of La₂O₃ would have enhanced the electron density of oxide ions and increased the ratio of non-bridging oxide ions. This is also consistent with the results of the refractive index, the average oxygen polarizability, and the oscillator strength of the La₂O₃-Ga₂O₃ glasses, as shown in Figs 3 and 5.

Figure 7: Unpolarized Raman scattering spectra for xLa₂O₃-(100 − x)Ga₂O₃ glasses.

The spectra were normalized at 180 cm⁻¹.

From the Raman spectra, it was also noticed that the maximum phonon energies of La₂O₃-Ga₂O₃ glasses were approximately 650 cm⁻¹. Compared with the maximum phonon energies of other oxide glasses, such as 1100 cm⁻¹ for silicate⁴⁰, 845 cm⁻¹ for germanate⁴¹, and 790 cm⁻¹ for tellurite glasses⁴², those of La₂O₃-Ga₂O₃ glasses were significantly lower and even corresponded to the lowest of all oxide glasses. Because the absorption in the IR range is caused by the vibration of phonons, the low maximum phonon energies should be a good explanation why La₂O₃-Ga₂O₃ showed much longer IR absorption edges than other oxide glasses. From the results of this study, the extraordinarily wide transparency range from the UV to the mid-IR realized in La₂O₃-Ga₂O₃ glasses should be due to the fact that these glasses contained neither network former oxides with high phonon frequencies nor heavy metal oxides with small optical energy gaps. When rare-earth ions are incorporated as phosphors, the low maximum phonon energy of the La₂O₃-Ga₂O₃ glass is also beneficial, because the multi-phonon decay rate of rare-earth ions in a glass strongly depends on the maximum phonon energy of the host. It is, therefore, expected that the low maximum phonon energies, large solubilities of rare-earth elements, and low OH⁻ content of La₂O₃-Ga₂O₃ glasses will even enable efficient mid-IR luminescence to be achieved³⁸, which cannot be obtained using typical oxide glasses with large multi-phonon relaxation rates.

Conclusion

This paper described the successful fabrication and fundamental properties of xLa₂O₃-(100 − x)Ga₂O₃ binary glasses. The glass-forming region was found to be 20 ≤ x ≤ 57. The refractive indices increased from 1.921 to 1.962, whereas the Abbe numbers showed no significant changes with x. Evaluation using the Lorentz–Lorenz relation revealed that the polarizabilities of the oxide ions were as high as 2.16–2.41 ų, indicating that the glasses were highly ionic. Optical transparency measurements revealed that the absorption edges in the UV and IR regions shifted towards shorter and longer wavelengths with x, respectively. The optically transparent range was from 270 nm to 10 μm in the 55La₂O₃-45Ga₂O₃ glass, which corresponds to the widest range of all oxide glasses. Raman scattering spectra indicated a decrease in bridging oxide ions and an increase in non-bridging oxide ions with increasing La₂O₃ content. The maximum phonon energy was significantly lower (~650 cm⁻¹) than that of other oxide glasses. These unique and superior characteristics suggest that La₂O₃-Ga₂O₃ glasses can be attractive host materials for various optical applications such as wideband transparent windows, achromatic lenses, or strong luminescent materials.

Methods

High-purity La₂O₃ and Ga₂O₃ powders were mixed stoichiometrically to form xLa₂O₃-(100 − x)Ga₂O₃ in a molar ratio. The mixtures were pressed into pellets under a pressure of 20 MPa and sintered at 1200 °C for 12 h in an air atmosphere. Pieces of approximately 50 mg taken from the broken pellets were vitrified in an aerodynamic levitation furnace. The specimens were levitated by an O₂ gas flow and heated by CO₂ lasers. A high-resolution, charge-coupled device camera was used to observe the levitated samples. Glass formation was confirmed by Cu Kα X-ray diffraction measurements. The compositions of the glasses were investigated by inductively coupled plasma–mass spectrometry (ICP-MS) analysis (Agilent Technologies Agilent 7700x).

T_g and T_p were determined by differential thermal analysis (DTA) in an air atmosphere at a heating rate of 10 °C/min (Rigaku Thermo plus EVO2 TG8121). All glasses were annealed at a temperature near T_g for 10 min in order to remove thermal strain prior to the physical property measurements. The densities of the glasses were measured using a gas pycnometer (Micromeritics AccuPycII 1340). For the optical measurements, the glasses were sliced and polished into disks approximately 1 mm thick. The refractive indices were measured using a prism coupler (Metricon Model 2010/M) at wavelengths of 473, 594.1, and 656 nm. The measured indices were fitted by the Drude–Voigt model shown in equation (1) using the least squares method, and the refractive indices and the abbe numbers were calculated from the fitted curves. The optical transmittance spectra were taken in the wavelength range of 250–700 nm using a UV-vis-NIR spectrophotometer (Hitachi High-Technologies UH4150). The IR transmittance spectra were taken in the wavenumber range of 400–4000 cm⁻¹ using a Fourier transform infrared spectrophotometer (Thermo Fisher Scientific Nicolet 6700). Unpolarized Raman scattering spectra were taken using a micro-laser-Raman spectrometer (JASCO NRS-7100) with excitation provided using an Ar⁺ laser at 488 nm.