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

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 Å3, 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.


Results and Discussion
shows the glass-forming region of the xLa 2 O 3 -(100 − x)Ga 2 O 3 binary system on the phase equilibrium diagram 25 . The glasses were obtained at 20 ≤ x ≤ 57. This is a slightly wider range than that of the La 2 O 3 -Al 2 O 3 binary system: 27-50 mol% La 2 O 3 14 . 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 30La 2 O 3 -70Ga 2 O 3 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 Δ T (= T p − T g ). T g showed a slight increase upon increasing x from 734 to 757 °C. The value of Δ T has been commonly used as a measure of glass stability. As can be seen in Fig. 2, all values of Δ T were less than 100 °C, indicating that the present glasses would be difficult to form using a conventional melt-quenching technique.
In most glasses, the glass-forming regions are close to the eutectic points 26 . The eutectic points in the La 2 O 3 -Ga 2 O 3 system, however, located at 23.1, 58.2, and 75.7 mol% La 2 O 3 do not correspond to the glass-forming region, as seen in Fig. 1. This situation is similar to the Y 2 O 3 -Al 2 O 3 13 and Ln 2 O 3 -Al 2 O 3 (Ln = Lu, Yb, Tm, Er, Ho, Dy, Tb, Gd, and Eu) systems 14 . 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 La 2 O 3 -Ga 2 O 3 system may be the absence of the LaGaO 3 phase in the metastable diagram, which is dominant in the actual devitrification process of the melt. In addition, it should be noted that Δ T 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 Ga 2 O 3 and La 4 Ga 2 O 9 were the dominant phases in crystallization, there should be only one eutectic point between these two phases and Δ T 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 La 2 O 3 -Ga 2 O 3 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 Ga 2 O 3 and La 4 Ga 2 O 9 phases, respectively. Furthermore, this crystalline phase is expected to be metastable because no stable phases were observed at this composition in the La 2 O 3 -Ga 2 O 3 phase equilibrium diagram. A detailed investigation of metastable phases in these systems will be the subject of future investigations.
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 La 3+ (1.052 Å 3 ) 28 and Ga 3+ (0.195 Å 3 ) 29 , α O2− values were obtained and are shown in Fig. 3(c). α O2− linearly increased from 2.16 to 2.41 Å 3 with increasing x. These values are rather large and correspond to those of Bi 2 O 3 -and TeO 2 -based glasses 30 . Therefore, La 2 O 3 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 La 3+ is 5 times larger than that of Ga 3+ . Nevertheless, the polarization in the La 2 O 3 -Ga 2 O 3 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 oxygen 19 . 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 cm 3 using Shannon's ionic radius (1.4 Å for O 2− ) 31 . Then, P O2− was obtained by dividing V O2− by 6.92 cm 3 . Figure 3(d) shows the compositional dependence of P O2− in xLa 2 O 3 -(100 − x)Ga 2 O 3 glasses. P O2− decreased linearly with x from 56.6 to 51.4%. Thus, glasses with higher Ga 2 O 3 content have more densely packed oxide ions. Figure 4 shows a comparison between xLa 2 O 3 -(100 − x)Ga 2 O 3 glasses and commercial optical glasses 32 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 xLa 2 O 3 -(100 − x)Ga 2 O 3 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, λ 0 , which reflect the average features of the oscillators in the glass 33 . 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, λ 0 is the inherent absorption wavelength, and λ is the wavelength of light. According to this relation, a plot of (n 2 − 1) −1 versus λ −2 is expected to be a straight line with a slope of (πmc 2 )/(e 2 Nf) and a y-axis intercept at (πmc 2 )/(e 2 Nfλ 0 2 ). Here, N    Figure 6(a) shows the optical transmittance spectrum of the 55La 2 O 3 -45Ga 2 O 3 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.
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).  Fig. 6(c). The transmittance was over 50% up until 7 μ m, and the absorption cut-off wavelength reached over 10 μ m. The slight absorption at approximately 3 μ m is due to the OH groups in the glass. The cut-off wavelength of the 55La 2 O 3 -45Ga 2 O 3 glass was much longer than those of typical oxide glasses such as silicate and borate 2 , slightly longer than those of heavy metal gallate glasses (8 μ m for PbO-Bi 2 O 3 -Ga 2 O 3 3 and 7.5 μ m for K 2 O-Ta 2 O 5 -Ga 2 O 3 glasses 6 ), and even close to those of fluoride glasses 38 . Figure 6   ions connecting two GaO 4 tetrahedra, respectively. Furthermore, the band at 300 cm −1 could be assigned to the vibration of the La-O bond 39 . 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 La 2 O 3 -Ga 2 O 3 glasses suggested that the ratio of non-bridging oxide ions increased, whereas that of bridging oxide ions decreased when La 2 O 3 was substituted for Ga 2 O 3 . This behavior agrees with the results obtained for the R 2 O-or R'O-Ga 2 O 3 glasses by Fukumi and Sakka 4 . However, they also suggested that non-bridging oxide ions appeared only when  the content of R 2 O or R'O was higher than 43 mol%. In La 2 O 3 -Ga 2 O 3 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 La 2 O 3 content than that of R 2 O-or R'O-Ga 2 O 3 glasses. On the other hand, Honma et al. evaluated the roles of La 2 O 3 in La 2 O 3 -P 2 O 5 binary glasses using XPS and Raman spectroscopies 28 . They showed that La 2 O 3 acts as a network modifier, enhancing the electron density of oxide ions and increasing the ratio of non-bridging oxide ions. Similarly, in La 2 O 3 -Ga 2 O 3 glasses, the high electron-donating ability of La 2 O 3 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 La 2 O 3 -Ga 2 O 3 glasses, as shown in Figs 3 and 5.
From the Raman spectra, it was also noticed that the maximum phonon energies of La 2 O 3 -Ga 2 O 3 glasses were approximately 650 cm −1 . Compared with the maximum phonon energies of other oxide glasses, such as 1100 cm −1 for silicate 40 , 845 cm −1 for germanate 41 , and 790 cm −1 for tellurite glasses 42 , those of La 2 O 3 -Ga 2 O 3 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 La 2 O 3 -Ga 2 O 3 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 La 2 O 3 -Ga 2 O 3 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 La 2 O 3 -Ga 2 O 3 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 La 2 O 3 -Ga 2 O 3 glasses will even enable efficient mid-IR luminescence to be achieved 38 , 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 xLa 2 O 3 -(100 − x)Ga 2 O 3 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 Å 3 , 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 μ m in the 55La 2 O 3 -45Ga 2 O 3 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 La 2 O 3 content. The maximum phonon energy was significantly lower (~650 cm −1 ) than that of other oxide glasses. These unique and superior characteristics suggest that La 2 O 3 -Ga 2 O 3 glasses can be attractive host materials for various optical applications such as wideband transparent windows, achromatic lenses, or strong luminescent materials.

Methods
High-purity La 2 O 3 and Ga 2 O 3 powders were mixed stoichiometrically to form xLa 2 O 3 -(100 − x)Ga 2 O 3 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 O 2 gas flow and heated by CO 2 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.