Glasses with high elastic moduli and high hardness values have been in demand for many years because the thickness of sheet glass with these properties can be decreased while maintaining its strength. Thinner and lighter glasses are desired for windows in buildings and cars, substrates for TFT displays and covers of smart-phones1,2,3. The elastic modulus and hardness of a glass can be estimated with relatively good accuracy using semi-empirical models based on ionic-pair potentials that consider the chemical composition, density and selected physical property data4,5,6. Particularly, the Young’s modulus E can be estimated using the Makishima and Mackenzie equation in which E is proportional to the atomic packing density and the sum of the partial dissociation energies of the components per unit volume4,5. The dissociation energies are in turn related to the bond strengths of the ionic pairs in the components. The Yamane and Mackenzie equation also indicates that the Vickers hardness (which is known to be directly related to the Young’s Modulus) is proportional to the square root of the bulk modulus K, shear modulus G and the bond strengths of the components7. Therefore, in order to achieve high elastic moduli and high hardness values, the use of components with large dissociation energies and a high atomic packing density are key factors.

Alumina (Al2O3) has one of the highest dissociation energies among the oxides (GAl2O3 = 131 kJ/cm3)4. Accordingly, high elastic modulus and high hardness glasses generally include large quantities of Al2O3, as is found in R2O3-Al2O3-SiO2 glasses (R = rare earth ion, Y, or Sc)8,9,10,11. These glasses also have high atomic packing densities. However, because Al2O3 is considered an intermediate oxide according to Sun’s glass formation criteria, the glass forming ability of a composition typically decreases as the quantity of Al2O3 increases12. In addition, compositions with a large amount of Al2O3 are often difficult to melt due to their high melting temperatures. These issues have limited the fabrication of bulk glasses with high elastic moduli and high hardness values. Recent progress in containerless processing has, however, allowed the vitrification of low glass forming materials, including those without added network formers such as TiO2-based, Nb2O5-based, WO3-based and Al2O3-based compositions, because heterogeneous nucleation from the melt can be avoided with this technique13,14,15,16,17,18. Thus, R2O3-Al2O3 glasses containing large quantities of Al2O3 have been prepared and found to exhibit superior mechanical properties as expected19,20. As a result, Al2O3-based glasses have attracted interest as high elastic moduli and high hardness materials. The properties of such glasses should be enhanced through the incorporation of additional components other than Al2O3 with high dissociation energies and high packing volumes. Herein, we describe the preparation of the new 54Al2O3-46Ta2O5 glass, which exhibits high elastic moduli and hardness values, using containerless processing. The thermal, optical and mechanical properties of the glass are also reported. In addition, an approach to the design of glasses with higher elastic moduli and higher hardness is proposed on the basis of the results of the local structure analysis around aluminum performed using 27Al MAS NMR spectroscopy.


Figure 1 shows the Differential Thermal Analysis (DTA) curve for the 54Al2O3-46Ta2O5 glass. The glass transition temperature Tg is located at 858 °C and the first TP1 and second TP2 crystallization peak are observed at 912 °C and 1054 °C, respectively. The difference between TP1 and TgT = TP1 − Tg) a measure of the thermal stability of the glass, is 54 °C, indicating the difficulty for vitrifying the glass using a conventional melting process. X-ray Diffraction (XRD) analysis confirmed that glass was totally amorphous and that the main phase of the crystallized sample after DTA was AlTaO4. The density of the annealed glass was ρ = 6.01 g/cm3. The composition of the glass samples measured by x-ray fluorescence (XRF) showed that the changes with respect to the nominal composition were less than 1 mol%. The microstructure of the fabricated glasses investigated through high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) is shown in Fig. 2. Observation through the HAADF-STEM has the advantage of achieving chemical contrast at the nanometric scale because it is very sensitive to the atomic number21. From the figure it can be observed that the glass is homogeneous at different scales and no phase-separation is observed. The randomly distributed bright points at the highest magnification are associated with the Ta atoms which have a much larger atomic number compared with the Al atoms (dark regions).

Figure 1
figure 1

DTA curve for the 54Al2O3-46Ta2O5 glass showing Tg and the first (TP1) and second crystallization peaks (TP2).

Figure 2
figure 2

HAADF-STEM images at different magnifications for the 54Al2O3-46Ta2O5 glasses.

Figure 3 shows the transmittance spectrum of the 54Al2O3-46Ta2O5 glass in the ultraviolet-visible (UV/vis) region. The glass was transparent in the visible region and had a maximum apparent transmission of 81%. The maximum theoretical transmittance was also estimated to be 81% using the equation Rmax = 1−[2R′/(1 + R′)], where R′ = [(nd − 1)/(nd + 1)]2 and the experimental refractive index nd value of the glass which was found to be 1.94. The estimated value was similar as that of the experimental result, indicating that the apparent transmittance value was to the result of losses only due to sample surface reflection and no light scattering occurred in the glass22. As observed in the inset of Fig. 3, the glass is colorless and transparent, which confirms that the valence state for all of the Ta ions is five and no Ta4+ ions are present23. The optical bandgap energy was estimated to be 4.3 eV using the UV absorption edge located at 288 nm.

Figure 3
figure 3

Transmittance spectrum of the 54Al2O3-46Ta2O5 glass in the UV/vis region. The inset picture shows the glass sample used for the transmittance experiment.

The measured longitudinal velocity VP and transversal velocity VS of the 54Al2O3-46Ta2O5 glass were 5.86 km/s and 3.20 km/s, respectively. From these values and the experimental density, it was found that the Young’s modulus E was 158.3 GPa, the bulk modulus K was 124.1 GPa, the shear modulus G was 61.5 GPa and the Poisson’s ratio v was 0.29. These values for the elastic moduli are considerably high and comparable to the maximum values in oxide glasses such as 40Y2O3-55Al2O3-5SiO2 and 28.5La2O3-71.5Al2O3, whose Young’s moduli were determined using Brillouin spectroscopy (169 GPa); however our measurement system showed that the Young’s modulus of those glasses were 145.5 GPa and 123 GPa respectively1,9,10. The Vickers hardness of the 54Al2O3-46Ta2O5 glass was 9.10 ± 0.05 GPa, which is also comparable to the maximum values reported for the oxide glasses; 81.8Al2O3-18.2Y2O3 (~9 GPa) and 29.3Al2O3-50.2SiO2-20.5Sc2O3 (9.4 GPa)20,24. Figure 4 shows indentation imprint for the 54Al2O3-46Ta2O5 glass at a load of 2.942 N. Extensive lines due to shear deformation on each face of the imprints are observed. In addition, at the same load, some of the imprints exhibited radial crack behavior25,26. No cracks were observed in any indentation below 1 N. The indentation cracking resistance (CR) was estimated to be 2.50 ± 0.13 N, which is comparable to a commercial Vycor glass27.

Figure 4
figure 4

Vickers indentation imprint at 2.943 N for the 54Al2O3-46Ta2O5 glass.

The 27Al MAS NMR spectrum of the 54Al2O3-46Ta2O5 glass is presented in Fig. 5. Although the spectrum is broad due to the amorphous nature of the glass, two distinctive peaks and a small shoulder were observed. These peaks and the shoulder were assigned to 4-coordinated Al (Al[4]), 5-coordinated Al (Al[5]) and 6-coordinated (Al[6]), respectively28,29,30. The spectrum was decomposed into the three components using the “dmfit” program applying a simple Czjzek model31,32. The thin dotted lines in the spectrum correspond to each of the components. The fitting, values for δiso (isotropic chemical shift), dCSA (width of the Gaussian distribution of δiso) and vQ* (quadrupolar product in kHz) were determined to be 64.8 ppm, 15 ppm and 1134 kHz for Al[4]; 36.7 ppm, 12 ppm and 985 kHz for Al[5]; and 10.3 ppm, 15 ppm and 973 kHz for Al[6], respectively33. Based on the integration of the peak areas, the fractions of Al[4], Al[5] and Al[6] were estimated to be 44.1%, 41.9% and 14.0%, respectively. The estimated average oxygen coordination number for Al was 4.7. The fractions of Al[5] and Al[6] were considerably larger than those observed in other aluminate glasses; Al typically forms AlO4 tetrahedra in MO-Al2O3 (M = Ca, Sr and Ba) glasses30. While Al[5] and Al[6] have been observed in some Al2O3-containing glasses, such as R2O3-Al2O3 (R is a rare earth ion or Y), R2O3-Al2O3-SiO2 and CaO-Al2O3-SiO2, the fraction of Al[5] has generally ranged from 3 to 30% and that of Al[6] from 1 to 2%24,34,35. The structure of the 54Al2O3-46Ta2O5 glass may therefore be due to not only the presence of AlO4 networks but also result in part from the high oxygen coordination of Al. The mechanism of glass formation with retention of large fractions of Al[5] and Al[6] is interesting and thus will be the subject of further investigations.

Figure 5
figure 5

27Al MAS NMR spectrum of the 54Al2O3-46Ta2O5 glass.

The total fitting curve corresponds to the sum of three Czjzek fitting curves: blue dots (Al[4]), red dashes and dots (Al[5]) and orange dashes (Al[6]).


These combined results indicate that the 54Al2O3-46Ta2O5 glass have good mechanical properties, high transparency and a high refractive, with an unconventional amount of Al[5] and Al[6] species. In order to understand the origin of the good mechanical properties of the glass the results are analyzed within the context of the Makishima and Mackenzie model e.g. the atomic packing density and dissociation energy per unit volume of the glass components.

The atomic packing density Cg was calculated from the density using the formula Cg = ρ(ΣxiVi)/M, where M is the molecular weight of the glass and xi is the molar fraction of the component i. The ionic volume Vi of an oxide is NA (4/3) , where NA is Avogadro’s number, m and n are the number of atoms in the AmOn oxide, rA is the ionic radius of the cation and rO is the ionic radius of oxygen. Shannon and Prewitt ionic radii were used36. The coordination numbers for Ta and O in the 54Al2O3-46Ta2O5 glass were assumed to be 6 and 2, respectively and the fractions of the coordination numbers for Al estimated from the results of the 27Al MAS NMR were used. The atomic packing density Cg was found to be 0.586, which is significantly larger than those for conventional oxide glasses (i.e., for SiO2 glass, Cg is 0.452). The small molar volume of Ta2O5 and the large fraction of highly coordinated Al are thought to contribute to the high packing density of the 54Al2O3-46Ta2O5 glass. It has been suggested that the formation of highly coordinated Al in aluminate glasses is promoted by the large cationic field strength, as observed in R2O3-Al2O3-SiO2 glasses8,9,10,11. Ta5+ also has large cationic field strength because of its small ionic radius and high valence state. Accordingly, Ta2O5 likely contributes to the high packing density of the 54Al2O3-46Ta2O5 glass via the formation of a large number of highly coordinated Al atoms.

A high content of Ta2O5 is also characteristic of the 54Al2O3-46Ta2O5 glass. The dissociation energy of Ta2O5 is substantially large (95.6 kJ/cm3)11. The elastic moduli of the glass were estimated using the Makishima and Mackenzie equation given by E = 2CgxiGi). Here Gi is the dissociation energy of each component oxide. Values of 131 kJ/cm3, 125 kJ/cm3 and 119.2 kJ/cm3 were used for GAl2O3 with Al in coordination of 4, 5 and 6 respectively11,37,38. The calculated Young’s modulus E of the 54Al2O3-46Ta2O5 glass was 131.9 GPa, which was approximately 17% less than the experimentally determined value, but still in relatively good agreement. A more accurate model may be necessary for estimation of the atomic packing density that includes the real contribution of the more highly coordinated cations. The energy contribution ratios of Al2O3 and Ta2O5 to the Young’s modulus were also estimated using the Makishima and Mackenzie equation and found to be 62% and 38%, respectively. It should be noted that the contribution of Al2O2 is not that high, while that of Ta2O5 is considerably high, which is unlike most other binary aluminate glasses with high elastic moduli. For example, a 28.5La2O3-71.5Al2O3 glass, which has one of the highest reported Young’s modulus values among the oxide glasses, has the following contribution: 16.71% from La2O3 and 83.3% from Al2O3. It has been previously accepted that a large contribution by Al2O3 is necessary to achieve a high elastic modulus for binary aluminate glasses, such as R2O3−Al2O3. However, a simple estimation of the energy contribution of the components in 54Al2O3-46Ta2O5 glass revealed that an appropriate component, like Ta2O5, can increase the elastic modulus even if the dissociation energy contribution of Al2O3 is small.

In summary, a glass with composition 54Al2O3-46Ta2O5 was fabricated using an aerodynamic levitation technique. Its glass transition temperature Tg was 858 °C and crystallization occurred at 54 °C above Tg, indicating a low glass forming ability. The glass is colorless and highly transparent in the visible region and has a refractive index nd of 1.94. The Young’s modulus E, bulk modulus K, shear modulus G and Poisson’s ratio v of the 54Al2O3-46Ta2O5 glass were determined via ultrasonic pulse-echo overlap analysis and were found to be 158.3 GPa, 124.1 GPa, 61.5 GPa and 0.29, respectively, while the Vickers hardness of the glass was found to be 9.1 GPa. These elastic moduli and Vickers hardness values are quite high and comparable to the maximum values of conventional oxide glasses. In addition, an indentation cracking resistance of 2.5 N was estimated from the indentation experiments. Furthermore, 27Al MAS NMR spectroscopic analysis revealed that the fractions of Al[4], Al[5] and Al[6] in the 54Al2O3-46Ta2O5 glass were 44.1%, 41.9% and 14.0%, respectively and the average oxygen coordination number of the Al cations was 4.7. Notably, the fractions of Al[5] and Al[6] are considerably large compared to those observed in conventional oxide glasses and may form because of the large cationic field strength of Ta5+. These results indicated that Ta2O5 was a key contributor to the high elastic moduli and high hardness values of the glass because the addition of Ta2O5 increases the packing density via formation of Al atoms that are highly coordinated with oxygen and because the Ta2O5 itself has a large dissociation energy. Moreover, a simple estimation of the energy contributions of the components in the 54Al2O5-46Ta2O5 glass using the Makishima and Mackenzie equation also suggested that the use of appropriate components can increase the elastic moduli even if the contribution of Al2O3 is small. These results provide insight into the design and fabrication of harder glasses based on both the local structure and the dissociation energies of the components.


Glass synthesis

Glasses were fabricated using an aerodynamic levitation furnace described elsewhere23. High-purity (99.99%) α-Al2O3 and Ta2O5 powders were mixed stoichiometrically with the chemical composition 54Al2O3-46Ta2O5, pelletized using a hydrostatic press and annealed at 1050 °C for 12 h in air. Pieces obtained from the crushed pellets were levitated in an oxygen gas flow and melted using two CO2 lasers at approximately 2000 °C. The melt was rapidly solidified by shutting off the lasers at a cooling rate of approximately 300 °C/s in order to obtain fully vitrified samples. The obtained spherical glasses (2 mm in diameter) were colorless and transparent. Glass formation was confirmed via Cu XRD analysis (Rigaku, RINT 2000). In order to rule out any compositional changes of the glass during the melting process, X-ray fluorescence experiments (JEOL, JSX-3100RII) were performed on glass samples under vacuum conditions. Glasses with composition 40Y2O3-55Al2O3-5SiO2, 28.5La2O3-71.5Al2O3 and 29.3Al2O3-50.2SiO2-20.5Sc2O3 were also fabricated using the levitation technique for comparative purposes.

Scanning transmission electron microscopy observation

In order to verify the homogeneity of the fabricated glasses observation with a scanning transmission electron microscope (JEOL, ARM-200CF) coupled with a high-angle annular dark field (HAADF) detector was performed. The microscope was equiped with a spherical aberration corrector (Ceos, Gmbh) and a cold field emission gun was used. The probe-forming aperture angle was 24.5 mrad while the HAADF and bright field (BF) detectors spanned through 68–280 and 0–17 mrad respectively. The spatial resolution of the present observation was approximately 0.1 nm. Glass powders were dropped into a perforated amorphous carbon films supported in Cu grids. No sputtering or heating was applied to the samples prior to the observation.

Thermal and physical properties

The glass transition temperature Tg and crystallization temperature Tp were determined via DTA at a heating rate of 10 °C/s (SII, TG6300). Prior to the analysis of the physical and structural properties, the glasses were annealed at 10 °C above the Tg in order to relax the stress introduced during quenching. The density ρ was determined using gas pycnometry (Micrometrics, AccuPyc II 1340). The experimental error associated with the density measurements was smaller than 0.01 g/cm3. The experimental densities for the 40Y2O3-55Al2O3-5SiO2, 28.5La2O3-71.5Al2O3 and 29.3Al2O3-50.2SiO2-20.5Sc2O3 glasses were 4.95 g/cm3, 4.22 g/cm3 and 3.04 g/cm3 respectively. The transmittance spectrum of an approximately 300 μm-thick sample was obtained in the range from 200 nm to 800 nm using a UV/vis spectrometer (Shimadzu, UV3100PC). The refractive index dispersion was determined via spectroscopic ellipsometry (J. A. Woolam, M-2000U).

Elastic moduli measurement

The pulse-echo overlap technique was used to obtain the ultrasonic velocities of the glass39. A 50 μm-thick ultrasonic transducer (LiNbO3 10 °Y-cut) and a 300 μm-thick glass were pasted at opposite corners of an edge truncated tungsten carbide (WC) block using a conductive epoxy resin. The ultrasonic echoes of the longitudinal P and shear S waves from the transducer were reflected by the glass and observed using a digital oscilloscope. The longitudinal velocity VP and transversal velocity VS were determined by dividing the thickness of the samples by the observed travel time of the waves. The longitudinal modulus L (C11) and shear modulus G (C44) were estimated using the equations and . The Young’s modulus E, bulk modulus K and Poisson’s ratio v were calculated using the equations E = G(3L − 4G)/(L − G), K = L − (4/3)G and v = (L − 2G)/(L − G), respectively. The obtained Young’s modulus E for the 40Y2O3-55Al2O3-5SiO2, 28.5La2O3-71.5Al2O3 and 29.3Al2O3-50.2SiO2-20.5Sc2O3 glasses were 145.6 GPa, 123 GPa and 133.2 GPa respectively.

Indentation behavior

Indentation experiments were performed on a Shimazu DUH HMV-1 Vickers tester at 23 °C and approximately 60% relative humidity. Optical-grade polished samples with a thickness of approximately 500 μm were used. The dwell time was set at 15 s. The Vickers hardness values HV were calculated from the diagonal lengths of the imprints at a load of 0.980 N. At least 20 indents were made for measuring HV. The indentation cracking resistance CR values were estimated from cracking probability curves using the method proposed by Wada et al.40. Here, CR is defined as the load required to generate two radial cracks on average or to achieve a 50% cracking probability. Each data point on the cracking probability curves developed in the present study also represents 20 indentation imprints. The reported value of CR was obtained by averaging the CR values determined from sigmoidal fittings of the cracking probability curves for three different samples. The imprints were observed by optical microscopy.

Al local structure

27Al MAS NMR spectroscopy of the glass was performed on a JEOL JNM-ECA 500 spectrometer equipped with MAS probe head at 11.74 T (500 MHz). The spinning rate was 15 kHz and a 4-mm-diameter zirconia rotor was used. The NMR spectra were recorded using π/6 pulses (0.4 μs) and a relaxation delay of 1 s and 4000–12000 signals were accumulated. The 27Al chemical shift δiso in parts per million (ppm) was referenced to an external 1 M AlCl3 solution (−0.1 ppm).

Additional Information

How to cite this article: Rosales-Sosa, G. A. et al. High Elastic Moduli of a 54Al2O3-46Ta2O5 Glass Fabricated via Containerless Processing. Sci. Rep. 5, 15233; doi: 10.1038/srep15233 (2015).