Structure of alumina glass

Abstract

The fabrication of novel oxide glass is a challenging topic in glass science. Alumina (Al₂O₃) glass cannot be fabricated by a conventional melt–quenching method, since Al₂O₃ is not a glass former. We found that amorphous Al₂O₃ synthesized by the electrochemical anodization of aluminum metal shows a glass transition. The neutron diffraction pattern of the glass exhibits an extremely sharp diffraction peak owing to the significantly dense packing of oxygen atoms. Structural modeling based on X-ray/neutron diffraction and NMR data suggests that the average Al–O coordination number is 4.66 and confirms the formation of OAl₃ triclusters associated with the large contribution of edge-sharing Al–O polyhedra. The formation of edge-sharing AlO₅ and AlO₆ polyhedra is completely outside of the corner-sharing tetrahedra motif in Zachariasen’s conventional glass formation concept. We show that the electrochemical anodization method leads to a new path for fabricating novel single-component oxide glasses.

Introduction

Oxide glasses, e.g., window glass, fiber glass, optical glass, and the cover glass of a smart phone are indispensable materials in our daily life. However, the fabrication of a novel single-component oxide glass is challenging particularly when a conventional melt–quenching method is used because the glass forming ability is governed by the viscosity of a high-temperature melt. Indeed, Angell proposed the concept of “fragility” to understand the relationship between the viscosity and the glass forming ability¹. The basic idea behind the formation of covalent glass is the corner-sharing tetrahedral motif proposed by Zachariasen in 1932². Sun classified single-component oxides into glass formers, glass modifiers, and intermediates³. SiO₂, B₂O₃, P₂O₅, and As₂O₃ are typical glass formers, in which the cation–oxygen coordination number is 3 or 4 and the glass network is formed by corner-sharing oxygen atoms. Alkali and alkali earth oxides are typical glass modifiers; they cannot form glass, but they can modify the network formed by a network former by breaking cation–oxygen bonds in the network and/or occupy voids^4,5. Alumina (Al₂O₃) can be considered as an intermediate, because it can be both a glass former and a glass modifier in binary oxide glasses, although Al₂O₃ cannot solely form glass.

Al₂O₃ has many applications, e.g., in cements, substrates of electronic materials, and high-temperature crucibles. As mentioned above, it is impossible to prepare Al₂O₃ glass by the melt–quenching method; hence, sol–gel methods were used to prepare amorphous samples for studying optical properties^6,7 and behaviors at high temperatures⁸. Another approach is the fabrication of thin films, such as the highly ductile amorphous Al₂O₃ thin films that have recently been reported⁹. However, the structure of amorphous Al₂O₃ is still largely unknown owing to a very limited number of structural studies. Lamparter and Kniep reported the formation of AlO₄ tetrahedra with corner-sharing oxygen atoms as confirmed by neutron and X-ray diffraction measurements with the aid of the reverse Monte Carlo (RMC)¹⁰ modeling technique¹¹. Hashimoto et al. reported the average Al–O coordination number of 4.7 determined by ²⁷Al nuclear magnetic resonance (NMR) spectroscopic measurements¹², whereas Lee and Ryu confirmed the formation of OAl₃ triclusters by ¹⁷O NMR measurements¹³. Shi et al. have recently reported the comparison between amorphous Al₂O₃ and liquid Al₂O₃, and they concluded on the basis of molecular dynamics (MD) and empirical potential structure refinement (EPSR)¹⁴ simulations based on diffraction data¹⁵ that the Al–O coordination number is increased in amorphous Al₂O₃.

In this study, we have found that amorphous Al₂O₃ synthesized by the anodization of aluminium metal shows a glass transition by differential thermal analysis (DTA). We have performed ²⁷Al solid-state NMR and high-energy X-ray and neutron diffraction measurements. Moreover, we constructed a structural model for the glass by a combined MD–RMC modeling technique to understand the structure of single-component intermediate oxide glass, because it is expected that the glass structure is inconsistent with Zachariasen’s rules.

Methods

Preparation of alumina glass

The Al₂O₃ sample was prepared according to our previous report¹². High-purity (99.99%) aluminium sheets were immersed in 1.25 mol dm⁻³ NaOH for 20 s at 60 °C, washed with tap water, immersed in 3.9 mol dm⁻³ HNO₃ for 60 s, and finally washed with deionized water to remove surface native oxides and contaminants. Constant-voltage anodization was performed for 80 V in 0.3 mol dm⁻³ H₂CrO₄ electrolyte for 2 h at 40 °C. After anodization, the sample was carefully washed with deionized water to remove residual electrolyte. A stepwise voltage reduction from formation voltage to ~ 60 V was performed in the same electrolyte to reduce barrier layer thickness. To detach the alumina from the aluminium substrates, anodic polarization was applied in a mixed solution of 1:4 vol% of perchloric acid (60%) and ethanol (99.5%) for 1 min at ~ 70 V. The detached sample was carefully washed with deionized water, dried at room temperature, and crushed into powder by an agate mortar. To remove physisorbed water, the powder sample was heat-treated at 300 °C for 4 h at a heating rate of 5 °C min⁻¹ and were subsequently cooled in the furnace, as previously reported.

Density measurement

The density measurement was performed on a helium pycnometer (AccuPyc 1340TC, Shimadzu-Micromeritics). Before the measurement, the sample was dried for 24 h at room temperature in vacuum.

DTA measurement

The differential thermal analysis (DTA) experiment was performed on a Rigaku Thermo plus EVO apparatus. The sample was dried at a heating rate of 10 °C min⁻¹ to 300 °C for 4 h and cooled in the furnace. After reaching 50 °C, the sample was heat-treated at a heating rate of 10 °C min⁻¹ to 1350 °C.

NMR measurements

The ²⁷Al magic angle spinning (MAS) nuclear magnetic resonance (NMR) experiment was performed on a JEOL JNM-ECA800 (18.79 T) spectrometer at a ²⁷Al Larmor frequency of 208.58 MHz. The sample was packed in zirconia rotors and spun at 20 kHz using a 3.2 mm HXMAS probe. The ²⁷Al chemical shift δ_iso in parts per million (ppm) was referenced to an external 1 mol dm⁻³ AlCl₃ solution (− 0.1 ppm). The ²⁷Al single-pulse MAS spectrum was obtained using 6/π pulses (0.67 us) with a recycle delay of 1 s and 512 scans. The spectrum was decomposed into three components, and fitting parameters, namely, the average isotropic chemical shift ($\overline{{\mathbf{\delta }}_{\mathbf{i}\mathbf{s}\mathbf{o}}}$), the width of the Gaussian distribution of δ_iso (ΔCS), and the average quadrupolar coupling constant ($\overline{{\mathbf{C}}_{\mathbf{Q}}}$), were determined using the “Dmfit” program¹⁶ applying a simple Czjzek model. The errors of fitting values for δ_iso and other parameters were < 0.04% and < 0.3%, respectively. The average N_Al–O was determined using the following equation: $\overline{{\mathit{N}}_{\mathit{A}\mathit{l}-\mathbf{O}}}=\sum \mathit{N}{\mathit{A}}_{\mathit{N}}$, where N and A_N represent the number of oxygen atoms around a given aluminium atom and the relative ratio of the corresponding peak area, respectively.

Diffraction measurements

The high-energy X-ray diffraction experiment was performed at the BL04B2 beamline at the SPring-8 synchrotron radiation facility, using a two-axis diffractometer dedicated to the study of disordered materials¹⁷. The energy of the incident X-rays was 61.4 keV. The raw data were corrected for polarization, absorption, and the background, and the contribution of Compton scattering was subtracted by using standard data analysis software¹⁷. The neutron diffraction measurement was conducted on a high intensity total diffractometer, NOVA¹⁸, installed at BL21 of the Materials and Life Science Experimental Facility at the J-PARC spallation neutron source. The wavelength range of the incident neutron beam was 0.12 Å < λ < 8.3 Å. The glass sample was transferred into vanadium-nickel null alloy cell 6 mm in diameter. The observed scattering intensity for the sample was corrected for instrumental background, attenuation of the sample and cell, and then normalized by the incident beam profile. All corrected data were normalized to give a Faber–Ziman¹⁹ total structure factor S(Q). A Lorch²⁰ modification function was used in Fourier transform.

Structure modelling

We combined MD simulation with NVT ensemble–reverse Monte Carlo (RMC) modelling for structure modelling. The MD simulation was performed using the LAMMPS package²¹ and RMC modellings were performed using the RMC ++code²².

In the case of l-Al₂O₃, we used the Born–Mayer-type pair potential in the MD simulation given as

$$\mathit{\varphi }\left({\mathit{r}}_{\mathit{i}\mathit{j}}\right)={\mathit{e}}^2\frac{{\mathit{q}}_{\mathit{i}}{\mathit{q}}_{\mathit{j}}}{{\mathit{r}}_{\mathit{i}\mathit{j}}}+{\mathit{B}}_{\mathit{i}\mathit{j}}\text{exp}\left(\frac{-{\mathit{r}}_{\mathit{i}\mathit{j}}}{{\mathit{R}}_{\mathit{i}\mathit{j}}}\right).$$ 1

Here, e is the elementary charge and B_ij and R_ij are the parameters accounting for the repulsion of ionic cells. q_Al =  + 3 and q_O =  − 2 are the charges of Al³⁺ and O^2–, respectively. The B_ij values of 2.3708 × 10⁻¹⁶ J (Al–O), 2.4031 × 10⁻¹⁶ J (O–O) and zero (Al–Al) and the R_ij values of 0.29 Å (Al–O and O–O) and zero (Al–Al) are found in Ref.²³. A random configuration composed of 10,000 atoms was prepared with respect to the experimental density (0.08630 Å⁻³). This configuration was heated to 5000 K and treated above 50,000 steps. Subsequentry, the configuration was cooled to 2400 K at a cooling rate of 1.3 K/ps. Eventually, the system was equilibrated at 2400 K for 100,000 steps. The long-range Coulomb interactions were calculated with standard Ewald summation and the simulation used periodic boundary conditions. A time step of 1 fs was used in the Verlet algorithm.

For g-Al₂O₃, the starting configuration, which contain 10,000 particles (Al, 4000: O, 6000) for g-Al₂O₃ was created using hard-sphere Monte Carlo (HSMC) simulation. The atomic number density is 0.09007 Å⁻³. The r-spacing for the calculations of the partial pair-distribution functions was set to 0.075 Å. Two kinds of constraints were applied: the closest atom–atom approach and the coordination number. The first one can avoid unreasonable spikes in the partial pair-distribution functions. The second forces aluminium atoms to coordinate to averaged 4.6 oxygen atoms within a cut off distance of 2.50 Å. After the HSMC simulation, RMC simulation was conducted to reproduce the X-ray S(Q) and neutron S(Q) data. Following the RMC simulations, the atomic configuration was optimized by MD simulation. The MD simulation was performed using pairwise additive interatomic terms of the form

$$\mathit{V}\left({\mathit{r}}_{\mathit{i}\mathit{j}}\right)={\mathit{e}}^2\frac{{\mathit{q}}_{\mathit{i}}{\mathit{q}}_{\mathit{j}}}{{\mathit{r}}_{\mathit{i}\mathit{j}}}-\frac{{\mathit{C}}_{\mathit{i}}{\mathit{C}}_{\mathit{j}}}{{\mathit{r}}_{\mathit{i}\mathit{j}}^6}+\mathit{D}\left({\mathit{B}}_{\mathit{i}},+,{\mathit{B}}_{\mathit{j}}\right)\text{exp}\left(\frac{{\mathit{A}}_{\mathit{i}}+{\mathit{A}}_{\mathit{j}}-{\mathit{r}}_{\mathit{i}\mathit{j}}}{{\mathit{B}}_{\mathit{i}}+{\mathit{B}}_{\mathit{j}}}\right),$$ 2

where the terms represent Coulomb, van der Waals, and repulsion energy, respectively. Here, r_ij is the interatomic distance between atoms i and j, D is a standard force constant 4184 JÅ⁻¹ mol⁻¹, q_i is the effective charge on atom i (q_Al = 1.17, q_O = − 0.78). The repulsive radius A_i values are 0.7852 Å (Al), 1.8215 Å (O); the softness parameter B_i values are 0.034 Å (Al), 0.138 Å (O); and the van del Waals coefficient C_i values are 36.82 ųkj^1/2mol^−1/2 (Al), 90.61 ųkj^1/2mol^−1/2 (O). The parameters A_i, B_i, C_i can be found in Ref.²⁴. The optimization of the atomic configuration was performed by minimizing the energy using the conjugate gradient method. We confirmed that these parameters are in better agreement with diffraction data; in particular, a very sharp principal peak (PP) in S^N(Q) for the glass was very well reproduced, while the parameters reported in Ref.²³ underestimated the PP.

After the MD simulations, both configurations were refined by additional RMC simulations while constraining the Al–O coordination number, and the partial pair-distribution functions, g_ij(r), within the first coordination shell to avoid unfavorable artifacts.

As a reference, we constructed three-dimensional structure model of g-SiO₂ by combined MD–RMC simulation. The MD simulation of SiO₂ glass was performed employing Born–Mayer type pair potentials, where the values q_Si and q_O are + 2.4 and − 1.2; the B_ij values were 21.39 × 10⁻¹⁶ J (Si–O), 0.6246 × 10⁻¹⁶ J (O–O) or zero (Si–Si); the R_ij values were 0.174 Å (Si–O), 0.362 Å (O–O) or zero (Si–Si)²⁵. As the initial atomic configuration, 9000 atoms (Si, 3000: O, 6000) were randomly distributed in a cubic cell with respect to the experimental number density (0.06615 Å⁻³). The simulation temperature was maintained at 4000 K for 20,000 time steps, then the temperature was reduced to 300 K over 200,000 time steps. Finally, the system was equilibrated at 300 K for 50,000 time steps. After the MD simulation, the obtained atomic configuration was refined by additional RMC simulation. In the RMC refinement, the MD results for the Si–O coordination number and the bond angle distribution for O–Si–O, and the partial pair-distribution functions within the first coordination distance were used as constraints. The cut off distance for the constraints for coordination of silicon and O–Si–O bond angle distribution was set to 1.90 Å.

Topological analyses

The bond angle distribution B(θ) was calculated as the number of bonds between θ and θ + Δθ, which is dependent on the solid angle ΔΩ ∝ sinθ subtended at that value of θ. Thus, each bond angle distribution was plotted as B(θ)/sinθ to compensate for the effect of ΔΩ. The primitive^26,27 (Al–O)_n ring size distributions for the g- and l-Al₂O₃ were calculated using the R.I.N.G.S. code^28,29. The void analysis was conducted employing the pyMolDyn code³⁰ with a cutoff distance of r_c = 2.50 Å.

Results and discussion

Figure 1a shows a DTA curve for an Al₂O₃ sample. Sharp intense and broad weak exothermic peaks at ~ 830 and ~ 1150 °C, respectively, are observed. The former peak is assigned to the crystallization of γ-alumina from the amorphous phase and the latter peak is assigned to the phase transition from γ- to α-alumina³¹. Note that the slight baseline shift to the endothermic direction is observed in the low temperature region around 500 °C (inset of Fig. 1a), owing to glass transition, showing that the sample is Al₂O₃ glass (g-Al₂O₃). The starting point of the shift, i.e., the glass transition temperature, is determined to be ~ 470 °C. In general, common glass‐forming oxides have a ratio of glass transition temperature to melting point (T_g/T_m) of ~ 0.67³². On the other hand, the present g-Al₂O₃ shows a T_g/T_m of ~ 0.32 (743 K/2345 K), which is extremely lower than that of general glass-forming oxides. The extraordinarily wide gap between T_g and T_m shows the low glass forming ability of alumina to maintain the deeply supercoiling state without the formation of crystal nucleus from the T_m = 2072 °C to T_g =  ~ 470 °C for realizing the glassy state.

Figure 1.

(a) DTA curve recorded at a heating rate of 10 °C min⁻¹ for g-Al₂O₃. (b) ²⁷Al solid state NMR spectrum for g-Al₂O₃.

Figure 1b shows a typical ²⁷Al single-pulse MAS NMR spectrum normalized by the total peak area. This spectrum consists of three broad peaks located at around ~ 64, ~ 36, and ~ 7 ppm, which are assigned to four- (AlO₄), five- (AlO₅), and six-fold (AlO₆) oxygen-coordinated polyhedra, respectively¹². This spectrum is decomposed into the three components and the fitting result (dotted curve) is in good agreement with the measured data (solid curve). The fractions of AlO₄, AlO₅, and AlO₆ are 37.5, 52.1, and 10.3%, respectively, and the average coordination number is determined to be 4.73. The values obtained here are slightly different from those of our previous report¹²; this variation depends on the resolution of the NMR equipment used. More precise values are obtained in the current study owing to the higher-resolution spectra obtained under higher magnetic fields. This precise local structural information is used as a constraint for the MD–RMC modeling as follows.

The mass density of g-Al₂O₃ is 3.05 g cm⁻³, which corresponds to the atomic number density of 0.0901 Å⁻³. This value is smaller than 4.00 g cm^-3 of α-Al₂O₃ and slightly larger than 2.92 g cm⁻³ of l-Al₂O₃³³. Note that the density of γ-Al₂O₃ is 3.59 g cm⁻³, which is between those of g-Al₂O₃ and α-Al₂O₃. This trend is very different from SiO₂, in which the density of glass (2.20 g cm⁻³) is comparable to those of α-cristobalite (2.30 g cm⁻³) and β-cristobalite (2.20 g cm⁻³), implying that a large density difference between the glass and crystal in Al₂O₃ indicates a low glass forming ability in single-component oxide glasses.

Figure 2 shows neutron and X-ray total structure factors, S^N,X(Q), for g-Al₂O₃ together with the results of MD–RMC simulation. For comparison, the results of silica glass (g-SiO₂)⁵ and liquid alumina (l-Al₂O₃) at 2400 K³³ are also shown. All the experimental S^N,X(Q) data are well reproduced by the MD–RMC simulations. The first sharp diffraction peak (FSDP)³⁴, which is from pseudo³⁵ (quasi³⁶) Bragg planes (successive small cages³⁷) created along a void, is observed at Q = 1.52 Å⁻¹ for g-SiO₂, a typical glass forming oxide, whereas the FSDP observed at Q ~ 2 Å⁻¹ is not prominent in g-Al₂O₃, suggesting the formation of a densely packed structure with a small void volume. In addition, g-Al₂O₃ shows an extraordinarily sharp PP³⁸ in the neutron S(Q), but no PP is observed in the X-ray S(Q) owing to the small weighting factor of O–O correlations for X-rays, because PP reflects the packing of oxygen atoms³⁹. Therefore, the extraordinarily sharp PP in the neutron S(Q), nearly twice sharper than those of l-Al₂O₃ and g-SiO₂, suggests the extremely high packing fraction of oxygen atoms manifested by the high density of g-Al₂O₃. A similar behavior is found in the neutron diffraction data of g-SiO₂ under a high pressure⁴⁰. Both the overall profiles of S^N,X(Q) for l-Al₂O₃ are broader than those for g-Al₂O₃, but the S^X(Q) data of both l-Al₂O₃ and g-Al₂O₃ are more identical, suggesting that O–O correlations are different between g-Al₂O₃ and l-Al₂O₃.

Figure 2.

(a) Neutron total structure factors, S^N(Q), together with the results of the MD–RMC simulations for g-Al₂O₃, l-Al₂O₃³³, and g-SiO₂⁵. (b) X-ray total structure factors, S^X(Q), together with the results of the MD–RMC simulations for g-Al₂O₃, l-Al₂O₃³³, and g-SiO₂⁵. Coloured curve, experimental data; black broken curve, MD-RMC model. Successive curves are displaced upward by 2 for clarity.

The neutron and X-ray total correlation functions, T^N,X(r), for g-Al₂O₃, l-Al₂O₃³³, and g-SiO₂⁵ are shown in Fig. 3. The first peak observed at 1.81 Å in T^N,X(r) for g-Al₂O₃ is assigned to the Al–O correlations. The second peak observed around 2.8 Å in T^N(r) and that around 3.2 Å in T^X(r) are assigned to the O–O and Al–Al correlations, respectively. Longer Al–O distances relative to g-SiO₂ and the asymmetric Al–O correlation peak with a tail of ~ 2.4 Å indicate the formation of distorted AlO_n polyhedra with a coordination number higher than 4. The average Al–O coordination number calculated using the area of the first correlation peak of T^N(r) is 4.6 ± 0.2, which is in agreement with the NMR result of 4.73 (37.5% of AlO₄; 52.1% of AlO₅; and 10.3% of AlO₆) and larger than 4.4 in l-Al₂O₃. Such a larger coordination number, which is often observed in nonglass-forming high-temperature oxide melts^37,41, cannot be observed in the typical glass-forming oxides. The overall profile for g-Al₂O₃ is similar to that for l-Al₂O₃, but the Al–O and O–O correlation peaks for g-Al₂O₃ are sharper than those for l-Al₂O₃, as apparently observed in T^N(r). This behavior suggests that the packing of oxygen atoms in glass could differ from that in high-temperature liquid.

Figure 3.

(a) Neutron total correlation functions, T^N(r), for g-Al₂O₃, l-Al₂O₃³³, and g-SiO₂⁵. (b) X-ray total correlation functions, T^X(r), or g-Al₂O₃, l-Al₂O₃³³, and g-SiO₂⁵. Upper and lower panel data were obtained by Fourier transform with Q_max = 25 and 18 Å⁻¹, respectively. Note that the Al–Al correlation peak is not legibly marked owing to its small weighting factor for neutrons.

Figure 4a shows the partial structure factors, S_ij(Q), derived from the MD–RMC models for g-Al₂O₃ and l-Al₂O₃ together with those for g-SiO₂. All the S_ij(Q) give a positive peak at the FSDP position in g-SiO₂, but there is no positive peak at the expected FSDP position in g-Al₂O₃. It is confirmed that the PP comprises the sum of positive correlations of A–A and X–X and negative correlations of A–X. As can be seen in Fig. 2b the PP is absent because the positive correlations of A–A and X–X are completely canceled by the A–X correlations in the S^X(Q) of g-SiO₂ and g- and l-Al₂O₃. On the other hand, the contribution of the X–X correlations at PP position is largely enhanced in the S^N(Q) (see Fig. 2a) due to large weighting factors of O–O correlations for neutrons. The positive O–O PP for g-Al₂O₃ is sharper than that for l-Al₂O₃, resulting in the exceptionally sharp PP observed in the S^N(Q) for g-Al₂O₃. Both the absence of the FSDP as mentioned above and the sharp PP in the S^N(Q) mainly originated from the O–O correlations allow us to expect the formation of the dense oxygen packing in g-Al₂O₃. The partial pair distribution functions, g_ij(r), derived from the MD–RMC models for g-Al₂O₃ and l-Al₂O₃ together with those for g-SiO₂ are shown in Fig. 4b. g-SiO₂ shows very prominent sharp Si–Si, Si–O, and O–O correlation peaks, whereas Al–Al, Al–O, and O–O correlation peaks are broader for g-Al₂O₃. Note that both the Al–O and O–O correlation peaks for l-Al₂O₃ are broader than those for g-Al₂O₃, whereas the Al–Al correlation peak in the former is identical to the latter. This trend is consistent with the finding that the difference in S^X(Q) between l-Al₂O₃ and g-Al₂O₃ is very small.

Figure 4.

(a) Partial structure factors, S_ij(Q), for g-Al₂O₃, l-Al₂O₃, and g-SiO₂. (b) Partial pair distribution functions, g_ij(r), for g-Al₂O₃, l-Al₂O₃, and g-SiO₂. A = Si or Al and X = O.

Table 1 shows coordination number distributions and polyhedral connections in g-Al₂O₃, l-Al₂O₃, and g-SiO₂. For a typical glass-forming oxide, g-SiO₂, the number of oxygen atoms around a Si atom (N_A–X) is 4, the number of Si atoms around an oxygen atom (N_X–A) is 2, and the SiO₄ polyhedra are connected via 100% corner-sharing, which is definitely in accordance with Zachariasen’s conventional glass formation concept. On the other hand, for g-Al₂O₃, more than 50% of the cations have N_A–X ≥ 5 and most of the oxygen atoms are connected with three Al atoms, showing the formation of OAl₃ triclusters and a significant number of OAl₄ tetraclusters. In addition, a significant fraction of edge-sharing AlO_n polyhedral units are observed in g-Al₂O₃. These features are completely inconsistent with Zachariasen’s rules. The fractions of AlO₅ and AlO₆ units, OAl₃ triclusters and OAl₄ tetraclusters, and edge-sharing AlO_n polyhedra are all characteristic features of a non-glass-forming behavior.

Table 1.

Coordination number distributions and polyhedral connections in g-Al₂O₃, l-Al₂O₃, and g-SiO₂.

	NA–X				NX–A				Polyhedral connection
	3	4	5	6	2	3	4	5	Corner	Edge	Face
g-Al2O3	0.0	46.0	42.0	12.0	9.2	71.5	18.7	0.6	79.4	19.3	1.3
l-Al2O3	2.3	56.7	37.3	3.7	15.7	73.7	10.5	0.1	82.3	17.6	0.2
g-SiO2	0.1	99.8	0.1	0.0	99.9	0.1	0.0	0.0	100	0.0	0.0

To obtain the characteristic real space atomic arrangement of intermediate oxide glass, we analyzed the bond angle distribution. Figure 5a shows the bond angle distributions of g-Al₂O₃ and l-Al₂O₃ together with those of g-SiO₂. The O–Si–O distribution has a well-defined peak at 109° attributable to the formation of regular SiO₄ tetrahedra. The Si–Si–Si distribution has a broad peak at around 109°, suggesting the formation of SiSi₄ hyper-tetrahedra⁴². The Si–O–Si distribution shows a peak at 165° attributable to the formation of the corner-sharing network. On the other hand, the bond angle distributions of g- and l-Al₂O₃ show completely different behaviors. The O–Al–O distributions of g-Al₂O₃ and l-Al₂O₃ shows peak at ~ 95 and ~ 180°, suggesting that AlO_n polyhedra are octahedral and are rather similar to those in non-glass-forming liquids, O–Zr–O in l-ZrO₂³⁷ and O–Er–O in l-Er₂O₃⁴¹. The Al–O–Al distributions has two peaks at 97 (edge-sharing) and 120° (OAl₃ tricluster) of g-Al₂O₃, which become a broad single peak in l-Al₂O₃ owing to highly densely packed structure. Both the O–Al–O and Al–O–Al distributions of g-Al₂O₃ are slightly different from the results recently reported by Shi et al., because they do not have neutron diffraction data¹⁵. The most striking difference between g-SiO₂ and g-/l-Al₂O₃ is the A–A–A distribution. The Si–Si–Si distribution suggests the formation of SiSi₄ hyper-tetrahedra probably associated with the prominent FSDP, but the Al–Al–Al distribution shows two peaks at ~ 60° and ~ 115°, suggesting that the distribution of Al atoms is due to a typical dense random packing⁴³, which cannot give rise to an FSDP in the diffraction data. The O–O–O distributions of g-Al₂O₃ and l-Al₂O₃ are also very different from that of g-SiO₂ and suggest that the distributions of oxygen atoms are dense also due to the random packing. Moreover, it is suggested that the oxygen packing fraction of g-Al₂O₃ increases owing to the higher mass density in the glass in comparison with the liquid (see Table 1). Indeed, the distribution peak of g-Al₂O₃ is sharper than that of l-Al₂O₃. Both the O–O–Al and O–A–Al distributions of g-Al₂O₃ and l-Al₂O₃ are also different from the O–O–Si and O–S–Si distributions in g-SiO₂.

Figure 5.

(a) Bond angle distributions for g-Al₂O₃, l-Al₂O₃, and g-SiO₂. (b) Primitive ring size distributions for g-Al₂O₃, l-Al₂O₃, and g-SiO₂. A = Si or Al and X = O.

To understand the topology of g-Al₂O₃ and l-Al₂O₃, we calculated the primitive ring size distribution and compared it with the g-SiO₂ data in Fig. 5b. g-SiO₂ shows a broad ring size distribution from threefold to ninefold rings, which is topologically disordered according to Gupta and Cooper⁴⁴. Both g-Al₂O₃ and l-Al₂O₃ show broad ring size distributions that are nearly identical, but they have large fractions of small rings, e.g., twofold rings (edge-sharing) and threefold rings, which is a signature of the low glass forming ability of Al₂O₃.

We show the atomic configuration of the glass obtained from the MD–RMC model in Fig. 6a to understand the structure of g-Al₂O₃. It is easily recognized that the assembly of two-membered rings (edge-sharing polyhedra) forms a lattice-like structure (black dotted line). The O–O atomic distance, which is the diagonal of one square, is ~ 2.3–2.7 Å, which is nearly consistent with the periodicity of ~ 2.3 Å estimated from the peak position of the PP observed in the S^N(Q) for g-Al₂O₃. Therefore, we conclude that, in addition to the large fraction of corner-sharing OAl₃ triclusters associated with the formation of octahedral AlO_n polyhedra, the larger fraction of edge-sharing AlO_n polyhedra for g-Al₂O₃ (19.3%) than for l-Al₂O₃ (17.6%) must be the origin of the exceptionally sharp PP observed in the S^N(Q) for g-Al₂O₃. We show the OAl₃ triclusters (red) and OAl₄ tetraclusters (yellow) in Fig. 6b. Such a cluster network can be found in g-SiO₂ at a high pressure of 200 GPa⁴⁵, but it is possible to fabricate such a glass structure at ambient pressure through the electrochemical anodization process under high electric field^46,47. The voids (highlighted in green) of g-Al₂O₃ are shown in Fig. 6c. The void volume ratio of g-SiO₂ according to our previous study is 32%⁵_, whereas those in g-Al₂O₃ and l-Al₂O₃ is only 4.5% and 5.5%, respectively, indicating that a highly densely packed structure is formed in them. The dense-random-packing-like bond angle distribution (see Fig. 5a) with significantly octahedral AlO_n polyhedra is very different from that of conventional oxide glass but rather similar to that of metallic glass in which icosahedra is highly distorted owing to geometric frustration⁴⁸.

Figure 6.

(a) Atomic configuration of g-Al₂O₃ (stick bonds schematic). (b) Atomic configuration of g-Al₂O₃ (schematic of the OAl₃ triclusters (red) and OAl₄ tetraclusters (yellow)). (c) Atomic configuration of g-Al₂O₃ with voids. Pink and red circles represent Al and O atoms, respectively, and green regions show the voids.

The electrochemically prepared g-Al₂O₃ has many features that are completely outside of Zachariasen’s rules. Regardless of the dense oxygen packing structure with a large fraction of edge-sharing polyhedral motifs, g-Al₂O₃ can stably exist as glass. The electrochemical anodization technique can be regarded as a powerful tool for our questing for novel intermediate oxide glasses with an extremely dense structure, and the comprehensive understanding of the atomic structure of the glasses will give new insights into the fabrication of novel glass materials.

Author contributions

S.K. and H.H. formulated the research project. H.H. prepared the materials. H.H. and K.Y. performed NMR measurements. H.H. and H.S. performed thermal analysis. Y.O. preformed neutron diffraction measurements and analyzed the measured data. S.K. and K.O. performed high-energy X-ray diffraction measurements and analyzed the measured data. Y.O. S.T., and S.K. performed MD–RMC modelling. Y.O., S.K., and M.M. analyzed the structural model. H.H., Y.O., and S.K. wrote the paper with the input of all the authors.

Competing interests

The authors declare no competing interests.