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(100−x)La2O3-xNb2O5 glasses with high refractive indices (>2.1) and low wavelength dispersion were prepared by containerless processing. All the glasses were colorless and transparent in the visible region. The glass forming region was divided into two regions: a high-La2O3-content (39 ≤ x ≤ 42) region and a high-Nb2O5-content (60 ≤ x ≤ 75) region. The dependence of the physical properties on the composition for these two types of glasses was different, implying that the high-La2O3-content glasses (La glasses) and high-Nb2O5-content glasses (Nb glasses) were intrinsically different. A large difference in the molar volumes of the two types of glasses indicated that the Nb glasses were more densely packed than the La glasses. Furthermore, the oxygen polarizabilities estimated from the molar volumes and refractive indices were greater than 2.43 Å3 for the La glasses, while those for the Nb glasses decreased from 2.43 Å3 with decreasing x. The large oxygen polarizabilities, as compared to those of conventional optical glasses, indicate a particularly high degree of ionic character for the component elements in the glasses. These results suggest that both the La and Nb glasses are desirable materials for high-valued optics, such as lenses with high power and high resolution as well as wide viewing angles used for a digital camera in a smartphone.
© 2014 Optical Society of America
1. Introduction
High refractive index glasses are essential components of lenses and enable the realization of high power and high resolution as well as wide viewing angles for digital cameras and microscopes. Therefore, the development of new glass compositions with higher refractive indices is of great interest to glass manufacturers. If a particular wavelength of the refractive index is not required, glasses with refractive indices >2 can be readily obtained though the addition of heavy metal ions, such as Bi3+ and Te4+ [1]. However, these glasses typically exhibit large wavelength dispersion and are colored because of absorption in the visible region. Accordingly, these glasses have chroma aberrations and focus light with different wavelengths onto different focal points and are not suitable for lenses that require high color reproducibility, irrespective of the refractive index being >2. Not only the value of the refractive index at a given wavelength but also the wavelength dispersion of the refractive index in the visible range should be considered.
Wavelength dispersion of the refractive index for optical glasses is evaluated using the Abbe number νd as described below:
where nd, nF, and nC are the refractive indices at 587.56 nm, 486.1 nm, and 656.3 nm, respectively. Greater wavelength dispersion results in smaller values of νd. Optical glasses are traditionally compared on an Abbe diagram with νd as the x-axis and nd as the y-axis [2]. Commercial optical glasses have values for nd in the range 1.5–2.0 and for νd in the range 15–100. The value of νd generally decreases when the value of nd increases. This means that high refractive index glasses typically exhibit large wavelength dispersion. Glasses with values nd ≥ 2 and νd ≥ 20 are desired materials for high-valued lenses; however, very few commercial glasses with these properties are currently available.Glass compositions are generally developed based on the glass forming rules proposed by Zachariasen [3] and Sun [4]. Glasses with desired properties are obtained by adjusting the amount of modifiers or intermediates added to network formers such as SiO2, B2O3, and P2O5. To increase the refractive index while retaining transparency in the visible region, addition of TiO2 or Nb2O5 as intermediates or La2O3 as a modifier is effective. However, these oxides can only be added to glasses at low concentrations because of their poor glass forming abilities. Recently, it was reported that compositions without any network formers could be vitrified in bulk by using containerless processing [5–12]. Containerless processing solidifies a levitated melt without any containers, and thus it suppresses inhomogeneous nucleation from the container walls. As a result, the deeply undercooled melt readily transforms to a glassy state, irrespective of the composition of the melt having low glass forming ability.
Using containerless processing, TiO2-based [13–18], Nb2O5-based [19,20], and WO3-based [21] high refractive index glasses have been prepared. The glasses are colorless and transparent and exhibit high refractive indices of 2.0–2.3 with low wavelength dispersion in the visible region. It is suggested that the high refractive indices of these glasses are attributed to large oxygen polarizabilities and densely packed structures [16,20]. Among these glasses, La2O3-Nb2O5 binary glasses have attracted much attention because of their two glass forming regions and the differences in the structures of the two types of glasses [20]. However, the physical properties have not yet been reported. In this paper, the thermal and optical properties of La2O3-Nb2O5 binary glasses are investigated.
2. Experimental procedures
Stoichiometric mixtures of La2O3 and Nb2O5 in the composition (100−x)La2O3-xNb2O5 (0 ≤ x ≤ 100) were sintered at 1000 °C for 12 h in air. Specimens of the sintered ceramics weighing approximately 20–40 mg were levitated using an O2 gas flow in an aerodynamic levitation (ADL) furnace and melted using a CO2 laser. The levitated melts were rapidly cooled to room temperature and solidified when the laser was turned off. Glass formation was confirmed by Cu Kα X-ray diffraction (XRD) measurements. The obtained glasses were colorless and transparent with high sphericity. Chemical analysis was performed by X-ray fluorescence spectrometer (JEOL, XRF JSX-3100RII). It was found that the composition of the glasses deviated <0.5% from the target composition. The glass transition temperature Tg and the crystallization peak temperature TP were determined using differential thermal analysis (DTA) at a heating rate of 10 K/min (SII, TG/DTA6300). Prior to measurement of the physical properties, the glasses were pre-annealed at a temperature slightly above the glass transition temperature in order to remove any internal stresses. The densities of the glasses were measured using a gas pycnometer (micrometrics, AccuPycII 1340). The transmittance spectra of glasses that were optically polished on both sides into approximately 500 μm thick were obtained in the wavelength range 300–2000 nm using a UV-vis spectrometer (Shimadzu, UV3100PC). The wavelength dispersions of the refractive indices were measured by spectroscopic ellipsometry (J. A. Woollam, M-2000F) in the wavelength range 300–1000 nm.
3. Results and discussion
Figure 1 shows the phase diagram for the (100−x)La2O3-xNb2O5 binary system. The compositions to which the ADL technique was applied are also shown in the diagram. The glass forming region was divided into two parts around two eutectic points: a high-Nb2O5-content region with 60 ≤ x ≤ 75 and a high-La2O3-content region with 39 ≤ x ≤ 42. These two glass forming regions are similar to those reported for (100−x)Ln2O3-xNb2O5 (Ln = La and Nd) amorphous ribbons fabricated by Kozuka et al. using a twin-roller quenching system [22]. They revealed that the glass forming regions were close to the eutectic points in the range 70 ≤ x ≤ 80 and in the vicinity of x = 40 for Ln = La, and only in the vicinity of x = 80 for Ln = Nd. Although there are slight differences in the glass forming regions for the bulk glasses and amorphous ribbons, they are similar to each other because the amorphous state was not obtained near other eutectic points.
Fig. 1 Glass formation region indicated in the (100−x)La2O3-xNb2O5 phase diagram. Circles, triangles, and crosses indicate glass, partially crystallized glass, and crystal, respectively. The range x = 35–45 is enlarged.
In most binary oxide glass systems, there is typically only one glass forming region, even if it is wide or narrow. Two glass forming regions have been observed only in a few binary systems, including Na2O-B2O3, BaO-TeO2, and Cu2O-TeO2 glasses [23]. It has been suggested that a stable crystalline phase between the two glass forming regions prevents glass formation for that composition, e.g., NaBO2, BaTe2O5, and Te3Cu2O7, respectively. In the case of the (100−x)La2O3-xNb2O5 binary system, crystalline LaNbO4 corresponding to x = 50 exists up to the liquidus line. Accordingly, the stability of LaNbO4 seems to prevent the melt from forming a glassy state, and thus divides the glass forming region into two separate regions. Furthermore, the differences in the previously proposed structures of the 60La2O3-40Nb2O5 and 30La2O3-70Nb2O5 glasses [20] may also encourage the division of the glass forming region.
Figure 2 summarizes the thermal properties (Tg and TP) for the (100−x)La2O3-xNb2O5 binary system. Both Tg and TP increased as the Nb2O5 content decreased. The Tg was ca. 750°C for the high-Nb2O5-content glasses (Nb glasses) and over 900°C for the high-La2O3-content glass (La glass). In addition, the dependence of the difference in TP and Tg (ΔT = TP − Tg) on the glass composition, which is a measure of the thermal stability of a glass, is shown in the inset of Fig. 2. The ΔT values for the Nb glasses are on a parabolic curve with a maximum value at x ~70, which indicates that the glass forming ability of 30La2O3-70Nb2O5 glass is higher than that of the other glasses. The largest glass spheres were obtained at this composition. However, the ΔTs of these glasses were so small that it was difficult to vitrify the composition in the bulk form using a conventional melting process.
Fig. 2 Glass transition temperatures Tg (circles) and crystallization temperatures TP (triangles) for the (100−x)La2O3-xNb2O5 glasses. The inset shows ΔT (Tg – TP); the dotted line is a guide for the eyes.
Figure 3 shows the dependence of the densities ρ and molar volumes Vm on the glass composition for the (100−x)La2O3-xNb2O5 binary system. The values for Vm were calculated using the equation Vm = M/ρ, where M is the molar weight determined from the glass composition per 1 mole of cations, such as 0.15La2O3-0.35Nb2O5. Crystalline LaNbO4, for which ρ = 5.91 g/cm3 and Vm = 25.02 cm3/mol, is also shown as a reference [24]. The densities were large and ranged from 5.47 to 6.09 g/cm3 because of the large amount of heavy La and Nb elements. In each glass forming region, ρ decreased linearly with increasing x. However, the respective fitted lines in the two regions were mismatched. When drawing an extrapolation line to x = 50 using the values for the La glasses, the extrapolated density was smaller than that of LaNbO4. In contrast, the extrapolated density obtained using the extrapolated line for the Nb glasses was larger than that of LaNbO4. This discrepancy was also seen for the compositional dependence of Vm. In the case of Vm, the extrapolated value at x = 50 using the values of the La glasses was larger than that of LaNbO4, while the extrapolated value for Vm obtained using the values of the Nb glasses was much smaller than that of LaNbO4. Considering that the density and the molar volume of a crystalline phase are generally larger and smaller, respectively, than those of amorphous materials when the composition is the same, the large ρ and small Vm of the Nb glasses clearly indicate a highly dense glass structure [20].
Fig. 3 (a) Densities and (b) molar volumes for the (100−x)La2O3-xNb2O5 glasses. The closed symbols correspond to the glasses and the open symbols correspond to crystalline LaNbO4. The dotted lines are fitted lines.
To investigate the significant differences in the compositional dependence of Vm for the La and Nb glasses, the partial molar volumes (VLa2O3 for La2O3 and VNb2O5 for Nb2O5) were determined [25]. These volumes were estimated using a least-squares fit to the equation Vm = (100−x)VLa2O3 + xVNb2O5. For the La glasses, VLa2O3 = 22.0 cm3/mol and VNb2O5 = 29.1 cm3/mol, while for the Nb glasses, VLa2O3 = 21.3 cm3/mol and VNb2O5 = 27.1 cm3/mol. Interestingly, the values for VLa2O3 were nearly the same for both regions, while the value of VNb2O5 for the Nb glasses was clearly smaller than that for the La glasses. These results indicate that when Nb2O5 is added to the glass, a niobium atom is squashed into a narrower space in the Nb glasses than in the La glasses. This simple picture is consistent with the results of structural analyses performed using X-ray and neutron diffraction, Raman scattering, and reverse Monte Carlo simulations [20].
Figure 4 presents the transmittance spectra for the (100−x)La2O3-xNb2O5 binary system in the UV-vis region. All of the glasses exhibited no absorption in the visible region, which indicates that the d–d transition of Nb4+ did not occur and all of the Nb ions had a valence state of 5 (d0). The maximum apparent transmission was approximately 70%, resulting from the large reflections from both sides of the surface due to its high refractive index. The absorption edge shifted to the UV region as the La2O3 content increased. The optical energy gap Eopt was then calculated from the spectrum near the optical absorption edge using a Tauc plot with the following relationship:
where α is the absorption coefficient, h is Planck’s constant, ν is the frequency of light, and A is an energy-independent constant. The inset of Fig. 4 shows the compositional dependence of Eopt, where Eopt increased from 3.36 to 3.85 eV as the La2O3 content increased. In this glass system, the Nb 5d and O 2p orbitals in the Nb-O bond are responsible for the valence and conduction bands. Therefore, the decrease in the density of states of the Nb 5d and O 2p orbitals accompanied with a decrease in Nb2O5 led to an increase in the bandgap. The differences in the densities and molar volumes may be the source of the differences in the compositional dependence of the bandgap for the La and Nb glasses.Fig. 4 Transmittance spectra for the (100−x)La2O3-xNb2O5 glasses. The inset shows the compositional dependence of the optical bandgap Eopt.
Figure 5 shows the refractive index dispersion of the (100−x)La2O3-xNb2O5 glasses as a function of wavelength. All of the glasses have refractive indices >2.1 in the visible region. According to the single oscillator model from the Drude–Voigt relationship, the refractive index n is expressed as a function of the wavelength of light λ using the following formula [26,27]:
where m and e are the electron mass and charge, respectively, c is the velocity of light, N is the number of molecules in the unit volume, f is the average oscillator strength, and λ0 is the inherent absorption wavelength. The value of N is calculated using the formula N = NAρ/M, where NA is Avogadro’s number, ρ is the density, and M is the molecular weight per 1 mole of cations. The parameters f and λ0 were used in this model as average features of oscillators, such as bridging oxygens, non-bridging oxygens, and cations. Based on this model, the plot of 1/(n2 − 1) versus 1/λ2 is expected to be a straight line with a slope of πmc2/e2Nf and a y-axis intercept at πmc2/e2Nf λ02. The values of λ0 evaluated using the linear relationship were 140, 150, 155, 164, and 168 nm for the x = 40, 60, 65, 70, and 75 glasses, respectively. An interpolation curve was produced using the parameters obtained and is shown together with the measured points. The interpolation curve corresponds to the measured value in the wavelength range above 350 nm indicates that the single oscillator model adequately describes the refractive index dispersion.Fig. 5 Refractive index dispersion for the (100−x)La2O3-xNb2O5 glasses. The inset shows the compositional dependence of the refractive index nd (circles) and Abbe number νd (triangles).
The Abbe number νd was estimated from the interpolation curves. The compositional dependence of nd and νd are shown in the inset of Fig. 5. νd increased as x decreased from 24 to 35. nd decreased linearly with decreasing x for the Nb glasses. The value at x = 40, extrapolated using the data for the Nb glasses, is 2.08, which is smaller than the measured value of 2.15. From these results, it is presumed that there is a different compositional dependence of nd between the Nb and La glasses in addition to the molar volume.
The origin of the high refractive index of this system was then considered with respect to the electronic states. The density, molar volume, and refractive index of a glass are related by the Lorentz–Lorenz equation:
where M is the molecular weight, Vm is the molar volume, αm is the molar polarizability, and NA is Avogadro’s number [28–30]. αm is composed of the polarizability of the cations αi and the oxygen ions αO2- using the following equation:where NO2- denotes the number of oxide ions in the chemical formula. The respective values for αLa3+ and αNb5+ are 1.052 Å3 and 0.242 Å3 [31,32]. Figure 6 shows the compositional dependence of αO2−. All of the αO2−values were >2.33 Å3 and were considerably large compared to those of conventional oxide glasses, such as silicate, borate, and phosphate glasses [28]. The large values for αO2− indicate that the oxide ions in the glass have a high electron-donating ability, and therefore the refractive index is predominantly governed by electrons around the oxide ions.Note that the αO2− value for the La glass was the largest value for all of these glasses, and αO2− decreased linearly with decreasing x in the Nb glasses. The value at x = 40 extrapolated using the data for the Nb glasses is 2.21 Å3, which is smaller than the measured value of 2.44 Å3. According to Eqs. (4) and (5), the nonlinear compositional dependence of αO2− is due to nd and Vm, because Σαi and NO2− vary linearly with the composition. Therefore, the rather large αO2− value for the La glass is due to the nd and Vm values, which were larger than those predicted using the values of the Nb glasses. The value of nd is dependent on the inherent absorption λ0; therefore, the larger nd is because of the larger λ0 that indicates a smaller optical bandgap. The observed optical bandgap, which was smaller than the estimated value obtained using the values for the Nb glasses, is shown in the inset of Fig. 4. However, the measurement accuracy for the optical bandgap was not sufficient in this case. On the other hand, the difference in Vm for the La and Nb glasses was obvious. From the partial molar volume, it was found that the local structure around Nb5+ in the two glass forming regions was different, while that for La3+ in the two regions was nearly the same. Accordingly, the difference in VNb2O5 caused the difference in αO2−, i.e. the spatial distribution of electrons in the glass. These results suggest that local structural differences around the Nb5+ in the La and Nb glasses enhanced the ionic nature of the La glasses compared to that of the Nb glasses, hence, resulting in retention of a high refractive index for the La glass, irrespective of the Nb2O5 content being small.
4. Conclusion
Binary (100−x)La2O3-xNb2O5 glasses were fabricated using a containerless processing and their physical properties were investigated. The glass forming region was divided into two regions: a high-Nb2O5-content region (39 ≤ x ≤ 42) and a high-La2O3-content region (60 ≤ x ≤ 75). The transmission spectra confirmed that these glasses were colorless and transparent in the visible region and the optical bandgap increased with increasing La content. The refractive index decreased and the Abbe number increased with increasing La content. The oxygen polarizability of these glasses was quite high indicating that they consist of highly ionic oxygens and cations, and that the refractive index is dominated by electrons around the oxygen ions. With respect to their potential application, it was noted that a high refractive index with low wavelength dispersion was realized for all of the glasses. In particular, the x = 40 glass had the largest Abbe number of 35 with a high refractive index nd of 2.15. In addition, the differences in the composition dependence of the physical properties, such as the thermal stability, density, molar volume, refractive index, and oxygen polarizability, for the La and Nb glasses strongly suggest that the La and Nb glasses are intrinsically different glassy states. The (100−x)La2O3-xNb2O5 binary glass system is therefore an important glass system for enabling both the further understanding of unconventional high ionic glass systems, such as TiO2-based, Nb2O5-based, and WO3-based glasses, and the production of revolutionary optical components.
Acknowledgments
This study was supported in part by the Nippon Sheet Glass Foundation, Iketani Science and Technology Foundation, Tokuyama Science Foundation, and Grants-in-Aid for Young Scientists (B) (19750174 and 23750236) and for Scientific Research (C) (21550185 and 25410236) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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