Deformability of Mg–aluminosilicate glass under high pressure and shear stress: dynamic coordination change of Al³⁺

Abstract

Deformation experiments were conducted on 20MgO–20Al₂O₃–60SiO₂ glass, which possesses superior mechanical properties, using a simple shear geometry under confining pressure. The glass exhibited densification, analogous to quasi-uniaxial compression, up to a shear strain of γ ≈ 1, and flow-dominated deformation at γ > 2. In the low-strain regime, densification was associated with a reduction in ring sizes and an increase in the coordination number of Al. Distinctive structural changes specific to shear deformation were also observed, including broadening of the T–O–T (T = Al or Si) bond-angle distribution and the formation of dangling bonds. A key mechanism proposed for flow involves higher-coordinated Al, formed during densification, dynamically changing its coordination number at the onset of flow. This transition from higher- to lower-coordinated Al is inferred to promote structural fluidity, while the concomitant transfer of non-bridging oxygens further enhances network flexibility. Overall, the results suggest that glasses capable of readily initiating local structural rearrangements can cooperatively enhance the fluidity of the entire network. This mechanism serves as an effective stress-dissipation mode, underpinning the observed high fracture toughness.

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Introduction

Glass is widely used in diverse applications owing to its transparency, high hardness, chemical durability, and low cost. Among various types, aluminosilicate glasses are extensively employed in commercial products because of their high Young's modulus and their ability to be chemically strengthened through ion exchange. Substituting part of the composition with MgO is known not only to improve the Young's modulus but also to markedly enhance fracture toughness and crack resistance, thereby imparting superior mechanical properties.^1,2 Understanding the deformation behavior of such glasses is essential not only for the development of new high-strength glasses but also for providing key insights into fields such as the materials science of disordered systems and planetary interior science.

Understanding fracture in glass remains a major challenge in materials science. Under different types of stress, such as hydrostatic and shear, glass undergoes deformation that can ultimately lead to fracture. Fundamentally, glass deformation involves two processes: densification and plastic flow. Indentation testing is the most common method for investigating these processes. However, indentation generates a complex stress field beneath the indenter, making interpretation difficult (e.g., pronounced densification under compression in the presence of shear³). Nevertheless, structural studies combining indentation with Raman spectroscopy have yielded valuable insights.^4,5 These studies, however, have predominantly focused on densification (the hydrostatic component), with only a few addressing plastic flow from a structural perspective. Since plastic flow is regarded as a key mechanism of stress dissipation, elucidating this process is critical for advancing the development of tougher glasses.

To elucidate the deformation behavior of glass under the complex stress fields encountered in practical applications, experiments under simplified stress conditions are highly effective. Among these, hydrostatic pressure studies have been extensively performed, primarily on silica glass and glasses of mineral compositions, yielding detailed insights into densification and its underlying mechanisms.⁶ It is well established that high pressure induces the reorganization of ring structures, and further pressure increases elevate the oxygen coordination number around Si atoms, thereby enhancing the glass density.⁷ In aluminosilicates, a pressure-induced increase in Al coordination has also been confirmed. This change occurs at lower pressures than for Si due to differences in ionic radii and significantly influences various physical properties.^8,9 For instance, in melts, the increase in Al coordination under pressure has been associated with a decrease in viscosity (e.g., in NaAlSi₃O₈ melt¹⁰). A flow model mediated by this higher Al coordination has also been proposed.¹¹ Research on the response of glass to shear stress has primarily relied on molecular dynamics simulations, which have reported both the reorganization of ring structures under simple shear (constant-volume) conditions¹² and the localization of deformation.¹³ Nevertheless, experimental investigations into the mechanisms of shear-induced deformation at room temperature remain limited, owing to significant experimental challenges.

In Earth sciences, deformation experiments are often conducted by applying simple shear stress to minerals under confining pressure (e.g., ref. 14). For brittle materials such as glass and minerals at ambient pressure, fracture is the dominant response to differential stress because the energy required for structural flow exceeds that required to create new surfaces. However, the application of confining pressure can invert this energy relationship, thereby suppressing fracture and promoting structural changes (i.e., flow). Evidence of such flow, referred to as “pile-up”, has indeed been observed in indentation tests on glass, indicating that a confining pressure component exists even within the stress fields encountered in practical applications.

In this study, we performed shear deformation experiments on glass under high pressure to investigate structural changes associated with the evolution of shear strain. A “multi-probe” analysis of the glass structure was conducted, spanning scales from the local atomic environment to the network topology, in order to gain insights into the dynamic structural rearrangements of aluminum ions during shear flow. Based on these results, we elucidate the factors contributing to the exceptional toughness of MgO-containing aluminosilicate glass.

Experimental

Sample preparation

The glass composition used in this study was 20MgO–20Al₂O₃–60SiO₂ (mol%). The raw materials were thoroughly mixed and placed in a Pt–Rh crucible, then melted at 1650 °C for approximately 22 h. After melting, the glass was cast onto a carbon plate. The cast glass was subsequently annealed at 850 °C (T_g + 30 °C) for 1 h and then slowly cooled to obtain bulk glass. The bulk glass was cut into wafers with a thickness of 250 ± 50 µm using a diamond cutter. Each wafer was core-drilled to a diameter of ϕ1.2–1.4 mm using an ultrasonic machine at a 45° angle. The core-drilled samples were then cut at the center using a 50 µm wire saw to insert a 15 µm-thick metal foil, which served as a strain marker.

High-pressure deformation experiment

The glass sample, prepared as described above, was positioned at the center of the high-pressure cell shown in Fig. S1. To apply simple shear stress, the sample was sandwiched between a pair of 45°-cut alumina pistons. Along the compression axis, SUS303 stainless steel and (Mg,Cr)O served as backing materials, and the applied shear stress was controlled by varying the thickness of these components. For further details of the pressure cell, see the SI.

The high-pressure cell was statically compressed at room temperature up to a confining pressure of 1.5 GPa using modified Paris–Edinburgh anvils, which constitute a quasi-uniaxial compression geometry. The pressure was ramped over 27.5 min. To achieve varying degrees of deformation, the samples were held at the target pressure for durations ranging from 5 min to 112 h. Subsequently, the pressure was released to ambient conditions within 7 min, and the recovered samples were subjected to various analyses. The applied pressure was determined using the calibration curve of Yamada et al.;¹⁵ however, it should be noted that this calibration was performed without a PTFE ring, which may slightly underestimate the actual pressure in the present experiments.

The samples for each experimental condition were prepared in multiple runs to measure shear strain and density. Samples for strain measurements, including the strain marker (see below), were used for measurement of birefringence and 2D X-ray scattering. Samples for density measurement were used for XANES, Raman spectroscopy, 1D X-ray total scattering and ESR measurement. Except for Raman spectroscopy, structural characterizations were performed after the density measurement, including a heating process below 50 °C.

The glass samples recovered from the high-pressure cell were polished to remove surface contamination from the Al₂O₃ pistons before each measurement. Approximately 10–50 µm of the surface layer was removed by first polishing with #3000-grit SiC abrasive paper, followed by polishing with a 0.5 µm-grit chromium oxide suspension.

Strain analysis

A cross-section of the recovered high-pressure cell assembly was embedded in resin, then polished. The resin-embedding process included heat-curing up to 140 °C. The inclination angle, θ, of the strain marker was measured using optical microscopy. The shear strain, γ, was then calculated from the relationship γ = tan(θ). The angle between the glass surface and the strain marker was measured at four points, and the average value was taken as the representative strain. The error in the strain measurement was estimated from the maximum and minimum values.

Evaluation of birefringence

Birefringence was measured at a wavelength of 543 nm using a polarized microscope (Nikon, Opti-Photo Pol) equipped with a Babinet compensator. Measurements were taken at five to six different points within the observable area of each sample. The average of these measurements was used as the representative birefringence value, and the error was defined as the range between the maximum and minimum values. Because a proportional relationship exists between birefringence and residual stress, mediated by the photoelastic constant, the measured birefringence can be interpreted as the residual stress within the sample.

Density measurement

The density of the recovered glass samples was measured using the temperature–sweep sink–float method. Each sample was immersed in a liquid of known density, and the temperature was gradually increased. The glass density was determined from the temperature at which the sample began to float, based on the density–temperature calibration curve of the immersion liquid. A mixture of 1,1,2,2-tetrabromoethane and 1,1,2,2-tetrachloroethane was used as the immersion liquid. Measurements were conducted over a temperature range of 15–50 °C. The change in glass density over this range is negligible (less than 0.1%, even for soda–lime silicate glass, which has a relatively high coefficient of thermal expansion). The experimental error was reported as the standard deviation of repeated measurements.

Al K-edge X-ray absorption near-edge spectroscopy

Al K-edge XANES measurements were carried out at the BL-13 beamline of the Ritsumeikan University SR Center. White synchrotron radiation was monochromatized using a KTP(011) crystal and directed onto the sample surface. Spectra were collected in fluorescence yield mode over an energy range of 1500–1750 eV using a silicon drift detector (SDD) positioned at 90° to the incident beam.

To determine the Al coordination number, the spectra were deconvoluted using a fitting model consisting of two main Gaussian peaks, corresponding to four-fold (^[IV]Al) and six-fold (^[VI]Al) coordinated aluminum at 1566 eV and 1568 eV, respectively. The model also included two arctangent step functions associated with these coordination states and a post-edge Gaussian peak.^16,17 Because a low-energy peak at 1563 eV was observed in the glass, which could not be assigned to ^[IV]Al, an additional pre-edge Gaussian peak was incorporated in this study. Fitting was performed over the 1560–1572 eV range, with the area ratio of the ^[IV]Al and ^[VI]Al Gaussian peaks constrained to match the height ratio of their corresponding arctangent functions. The uncertainty in the determination of Al coordination using this method is approximately 2–4%.^16,17

Raman spectroscopy

Raman spectra were collected using a JASCO NRS-5100 spectrometer with an excitation wavelength of 532.5 nm. For each sample, five spectra were acquired from different locations within a 50 µm radius at the center of the glass, and these were averaged to obtain the representative spectrum. The spectra of the deformed samples exhibited a broad background feature, which was corrected by baseline subtraction, as shown in Fig. S2.

1D X-ray total scattering for PDF analysis

High-energy X-ray total scattering measurements were carried out on both the as-prepared and deformed glass samples using an angle-dispersive method at the BL04B2 beamline of SPring-8.¹⁸ Monochromatic X-rays with an energy of 61.2 keV were employed. The X-ray scattering patterns were collected over a diffraction angle (2θ) range of 0° to 48.6°. The raw intensity data were normalized using atomic scattering factors, and after subtracting the Compton scattering contribution, the structure factor, S(Q), was derived. Subsequently, the total correlation function, T(r), was obtained by applying a Fourier transform to S(Q).¹⁹

2D X-ray total scattering for anisotropy analysis

Two-dimensional (2D) X-ray total scattering measurements were carried out using a micro-focused X-ray diffractometer (Rigaku, R-Axis Rapid-II) with a Cu X-ray source (λ = 1.54184 Å) operated in transmission geometry. The incident beam, focused by a mirror, was collimated to a spot size of ϕ = 100 µm immediately before the sample. For the primary analysis, the X-ray beam was incident parallel to the shear plane (i.e., from the front to the back of the page in Fig. S1). All samples were thinned to 300–400 µm to minimize variations in X-ray absorption and angular resolution due to differences in thickness. To evaluate the structure within the shear plane, one sample was also measured with the beam incident perpendicular to the shear plane.

The scattered X-rays were collected using a curved digital imaging plate (IP) detector. The raw curved data were corrected to obtain flattened images using analysis software (Rigaku, Curve2Flat). One-dimensional (1D) diffraction patterns were then extracted from the 2D data in 10° azimuthal angle (ψ) increments using IPAnalyzer and PDIndexer.²⁰ The azimuthal variation of the first sharp diffraction peak (FSDP) was fitted with a cosine function to determine the angles corresponding to maximum (Q_max) and minimum (Q_min) intensity.

Electron spin resonance measurement

Electron spin resonance (ESR) measurements were carried out using a Nikkiso ES-10 spectrometer operating in the X-band (∼9.4 GHz). The microwave power was set to 0.36 mW. The magnetic field and signal intensity were calibrated using the absorption lines of a Mn²⁺/MgO standard corresponding to g-values of 2.034 and 1.981.

Baseline correction was applied to the acquired spectra, and spin concentrations were quantified by double integration of the signal. Samples were inserted into silica glass tubes for measurement; the intrinsic defect concentration of the sample tubes was approximately 3 × 10¹⁶ spins g⁻¹. Absolute spin concentrations were quantified using TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl) as an external standard. Calibration curves were constructed from solutions of TEMPOL in dehydrated benzene at varying concentrations. All measurements were carried out at room temperature.

Results and discussion

Deformation behavior

When shear stress was applied to the glass under high pressure, large birefringence (≈3 × 10⁻⁴) was observed in the region of shear strains γ < 1 (Fig. 1a). The birefringence decreased with increasing shear strain, dropping to less than one-third of its initial value at γ > 3. In addition, a change in the orientation of the birefringence axis was observed at γ ≈ 2. In the low-strain region, the fast axis of birefringence was aligned with the compression axis (Fig. 1a, squares), whereas in the region of γ > 2, it shifted to a direction perpendicular to the compression axis (Fig. 1a, circles). Furthermore, samples with γ > 2 exhibited localized deformation (e.g., Fig. 1c, black arrows), which appears to represent a deformation mode different from the uniform deformation observed at γ ≤ 1 (Fig. 1b).

Fig. 1 (a) Change in birefringence (Δn; black squares and circles) and density (red triangles) as a function of shear strain (γ). Squares and circles indicate the fast and slow axes of retardation, respectively, relative to the compression axis. Open symbols are taken from a previous study.²¹ (b) and (c) Cross sectional images of the samples marked (b) and (c) in figure (a). The black arrow indicates the shear band (strain localization).

The glass in this study is inherently isotropic and does not exhibit birefringence. Previous NMR studies on glasses of the same composition have shown that 94% of Al atoms adopt four-fold (^[IV]Al) coordination.⁹ Because the RO/Al₂O₃ ratio is 1, approximately 94% of Mg²⁺ ions serve as charge compensators for Al. The structure contains very few non-bridging oxygens or highly coordinated Al atoms, and the glass mainly consists of tetrahedral SiO₄ and AlO₄ units, resulting in a highly polymerized network. A study on borosilicate glass revealed that birefringence originating from structural anisotropy is strongly induced by anisotropic structural units and their alignment.²² In contrast, a highly polymerized network structure composed of tetrahedral units hardly exhibits birefringence. This is because of both the inherent isotropy of the tetrahedral units and the fact that the high rigidity of the network prevents structural orientation. Therefore, the large birefringence observed at γ ≤ 1 is attributed not to orientation-induced birefringence but to a photoelastic effect. Indeed, the orientation of the fast axis reflects residual compressive stress, indicating that the glass has deformed in a manner similar to uniaxial compression. Previous report²¹ has confirmed that at γ ≈ 1, the glass thickness decreases by approximately 35%, and the density increases by approximately 5%. This region can thus be considered a deformation regime involving both densification and plastic flow (sub-simple shear).

In contrast, in the region of γ > 2, birefringence decreased to approximately 1 × 10⁻⁴, suggesting relaxation of residual stress. Moreover, the orientation of the fast axis rotated by roughly 90°, strongly indicating a deformation mechanism different from that of uniaxial compression. Previous study²¹ also reported that, in the range γ = 1–4, the thickness reduction was only 5–10%, and the density increase was approximately 1%. In situ stress–strain observations revealed a sharp drop in deformation stress around γ ≈ 1. Additionally, for γ > 2, the inclination of the strain markers varied spatially, indicating localized deformation. Taken together, these results suggest that shear strains of γ = 2–4 are dominated by plastic flow, whereas the region γ = 1–2 represents a transitional regime from densification-coupled plastic deformation to plastic flow.

A more detailed examination of strain evolution reveals that, under higher shear stress conditions (hard backing: “Higher stress” in Fig. 2), the strain increases progressively with dwell time (Fig. 2, inset). In contrast, under lower shear stress conditions (soft backing: “Lower stress” in Fig. 2), the strain remains nearly constant over time. This behavior suggests that the glass exhibits characteristics of a Bingham fluid, requiring a yield stress to initiate flow. Accordingly, the flow observed at γ > 2 can be classified as visco-plastic. At lower strains, the response is primarily plastic with negligible time dependence. The reduction in strain rate at γ > 4 is not intrinsic but stems from limitations of the high-pressure cell; the setup caps deliverable strain, and beyond that cap the measurement saturates, giving the appearance of a lower strain rate.

Fig. 2 Dwell time dependence of shear strain. The stresses labeled as “Higher” and “Lower” in the figure were controlled by changing the backing thickness of the Al₂O₃ piston and backing materials (see Fig. S1). The inset shows an enlarged view of the dwell time range from 0 to 20 hours. Dashed lines represent fitting results for t = 0.083–4 h (orange), 4–67 h (blue), and 20–112 h (black). Data for “Higher stress” were taken from a previous study.²¹

Modification of Al coordination via deformation

The XANES spectrum of the as-prepared sample is dominated by a main peak at approximately 1566 eV (Fig. 3), corresponding to four-fold coordinated Al (^[IV]Al).²³ Broad shoulder at ≈1570 eV corresponds to the contributions both ^[VI]Al and multiple scattering.^17,23 Upon deformation to a strain of γ = 0.9, a shoulder emerges near ∼1568 eV, consistent with octahedrally coordinated Al (^[VI]Al)²³ and indicating an increase in the average Al coordination number. Five-coordinated Al³⁺ species (^[V]Al) are widely recognized to occur in glasses,^24,25 and our analysis likely counts such potentially five-coordinated Al³⁺. With further strain beyond γ = 0.9, the intensity of this shoulder decreases. Notably, at γ = 3.9, the spectrum is almost identical to that of the as-prepared glass, although it exhibits a slightly narrower bandwidth. As the strain evolves further, although the absorption near 1568 eV remains slightly higher than that of the as-prepared sample.

Fig. 3 Al K-edge X ray absorption spectra of as made and deformed glasses. Dotted lines indicate absorption peak position of four- and six-coordinated aluminum ion.

Following the procedure of previous studies,^16,17 the Al coordination number was estimated from changes in XANES peak areas as a function of shear strain (results of peak deconvolution are shown in Fig. S3 and Table S1). The proportion of ^[VI]Al was approximately 12% and 25% in the as-prepared and γ = 0.9, respectively. However, previous studies for the glasses and melts reported that the proportion of ^[V]Al was initially increased by applying pressure,^9,26 then ^[VI]Al was increased with higher pressure. Our analysis should include the contribution of ^[V]Al, in fact, ^[V]Al peak in X-ray absorption and fluorescence spectra appears between ^[IV]Al and ^[VI]Al, e.g. andalusite.^23,27 To involve formation of ^[V]Al, ^[VI]Al proportion was converted to average coordination number of Al (Fig. 4).

Fig. 4 The average coordination number of aluminum ions as a function of shear strain, γ. Data from Neuville et al.²⁵ was extracted from their reported figure. The error in the Al coordination of our results is 2%, which is reported in Kato et al.¹⁷

Average CN of as-made sample (γ = 0) from XANES spectra is consistent with earlier reports of this composition.^2,9,25 The average CN increased and reached a maximum at γ ≈ 1, decreased at γ ≈ 4, and then exhibited a tendency to increase again. This trend suggests that higher-coordinated Al is generated during the initial densification stage of deformation. At larger strains, the deformation mode shifts toward flow (see Fig. 1, densification and birefringence), accompanied by a reversion of Al to lower coordination states. Therefore, changes in Al coordination are not stable but instead represent a dynamic structural response to shear deformation. Because the measurements were performed after recovery at ambient pressure, it is possible that an even larger fraction of highly-coordinated Al existed during the deformation process.

One possible hypothesis is that the increase in the average CN at γ = 0.9 could be associated with a lack of bond rearrangement under this small-strain condition, as implied by the large residual stress (Fig. 1). This residual stress, which corresponds to bond strain, could result from the retention of unstable structures, such as highly-coordinated Al. In contrast, bond rearrangements are expected to occur frequently during shear flow, leading to a decrease in residual stress. This suggests that a stable structure is mainly formed through structural relaxation. Furthermore, the degree of densification and the change in average CN in a previous hydrostatic compression study are consistent with our results. For instance, that study reported a 6% densification with a 0.2 increase in average CN, which is similar to our observation of 7% densification with a 0.25 CN increase. This similarity implies that the glass structure tends to transition toward a relatively stable state as it moves from the low-strain to the high-strain region, i.e. average CN decreases as a strain increases.

A small amount of initially present NBO can promote an increase in the average CN. For instance, it is known that CaO–Al₂O₃–2SiO₂ glass, which is stoichiometrically NBO-free, can actually contain approximately 5% NBO.²⁸ Especially under the pressure conditions investigated in this study, such NBO can drastically affect the pressure-induced increase in aluminum coordination number via a process that consumes NBO.²⁹ However, the presence of 5% NBO is insufficient to account for the total increase in average CN observed in our results. Assuming the initial presence of 5% NBO, these NBOs would have to be almost completely consumed to account for the total increase in average CN observed in our results. However, Raman spectra indicated the formation of NBOs during deformation (discussed later). This contradiction suggests that, in addition to the initial NBOs, the generation of NBOs, which occurs as a counterpart to the formation of oxygen triclusters,^28,30 during deformation contributes to the coordination change.

Compared with previous reports on silica and other aluminosilicate glasses subjected to hydrostatic pressure at room temperature, our results demonstrate that higher-coordinated Al forms at much lower pressures. For example, in Mg₃Al₂Si₃O₁₂ (pyrope) glass, which contains ≈17% of NBO stoichiometrically, an increase in Al coordination number was observed even after decompression from pressures up to approximately 5 GPa.³¹ Therefore, the appearance of higher-coordinated Al at low pressure in this study is attributed to structural changes induced by plastic deformation under the combined action of shear stress and pressure.

Modification of the aluminosilicate network

In the Raman spectra of the shear-deformed samples (Fig. 5), significant broadening was observed in the main band at 430–500 cm⁻¹. This band is attributed to T–O–T bending vibrations.³² Although a sharp peak at approximately 490 cm⁻¹, corresponding to the so-called D1 band from four-membered rings of TO₄ tetrahedra, has been reported in silica glass,³³ no such peak was observed in the present glass, indicating that the main contribution to the band arises from T–O–T bending vibrations. Model calculations have shown that the central frequency of the bending vibration correlates with the T–O–T bond angle,³⁴ and experiments under hydrostatic compression also confirm this correspondence.³⁵ Under hydrostatic pressure, the main band sharpens and shifts to higher wavenumbers with densification due to a reduction in both the bond angle and its distribution. In contrast, the broadening observed in this study reflects an increase in the bond angle distribution, indicating a characteristic structural change induced by shear stress. Additionally, a pronounced increase in scattering intensity was detected at 600 cm⁻¹. This band, which is called as D2 band, is assigned to three-membered rings of TO₄ tetrahedra.^33,35 The intensity of this band increased with increasing strain, suggesting that larger ring structures are being broken and smaller three-membered rings are formed. Notably, the intensity increase at 600 cm⁻¹ was approximately 14% at γ = 0.9 and 38% at γ = 5.5. This increase shows a roughly linear correlation with the densification rather than with the shear strain.

Fig. 5 Variation of the Raman spectra with shear strain, γ. Solid circles and diamonds indicate the scattering assigned to D2 band (≈600 cm⁻¹) and Q⁴ speciation (≈1150 cm⁻¹), respectively. An edge at ≈ 1100 cm⁻¹ in γ = 0.9 is an artifact from the apparatus.

With increasing strain, changes were also observed in the high-frequency region of the Raman spectra. Specifically, an increase in scattering intensity near 950 cm⁻¹ (Q²)³⁶ and a decrease near 1150 cm⁻¹ (Q⁴)³⁶ were detected, where Qⁿ denotes the number of bridging oxygens. These changes in Q-species may be associated with the formation of tricluster oxygens. The formation of tricluster oxygens has been proposed in studies of glass structural models³⁷ and investigations of melt viscosity.^30,38 The XANES results further suggest that changes in Q-species could arise from the formation of higher-coordinated Al. That also implies the existence of NBOs in the glass structure, since an increase in coordination typically involves the consumption of NBOs. Additionally, molecular dynamics simulations of shear-deformed glasses have reported an increase in scattering intensity around 900 cm⁻¹.¹² Therefore, the changes observed in the high-frequency region in this study are considered to arise from the formation of non-bridging oxygens associated with tricluster formation and from structural distortions induced by the applied shear stress.

Defect induced by shear deformation

Two distinct peaks were observed at g = 2.002 and 2.001 (Fig. 6). Defect peaks were also detected in the as-made glass due to contributions from defects in the sample container. The peaks originating from the sample are consistent with the g-values of E′ centers, which correspond to dangling bonds within SiO₄ tetrahedra.^39,40

Fig. 6 ESR spectra of the blank (without sample), as-made glass, and deformed glasses are shown. All spectra, including contributions from the sample container (blank), exhibit two positive peaks and one negative peak corresponding to E′ centers.

Quantification of spin concentrations revealed that, in the sample deformed to γ ≈ 1, the defect concentration increased by approximately 50% compared to the as-made glass (Fig. 7). In a related manner, glass grinding has been shown to introduce E′ centers into the structure.⁴¹ In samples subjected to higher strains, the defect concentration decreased, returning to levels comparable to those of the as-made glass. This suggests that shear flow reduces bond strain, as the associated structural relaxation transforms the glass structure from a metastable state to a more stable configuration. Supporting this observation and consideration, many cracks were observed in the recovered glass at low strains, suggesting the presence of significant residual stress. However, the concentration of dangling bonds at γ = 5.5 was similar to that at γ = 0.9 despite its small birefringence. This result may be influenced by the axial stress in this high-strain region, acting in a manner similar to the uniaxial-like compression observed at γ = 0.9.

Fig. 7 Defect concentration with shear strain, γ. The result includes a noise about 3 × 10¹⁶ spins g⁻¹, which is estimated from blank measurement.

Additionally, a fluorescence-like background appeared in the Raman spectra (Fig. S2), with an intensity maximum at 2200 cm⁻¹ (2.04 eV) and a full width at half maximum of 0.22 eV. These values are close to those reported for non-bridging oxygen hole centers,⁴² implying the formation of oxygen dangling bonds. Taken together, the ESR and Raman fluorescence band results indicate that a portion of the Si–O bonds broken during shear deformation did not re-bond and remained as dangling bonds. Because these bond states are inherently unstable, an even higher concentration of dangling bonds likely exists during the deformation process.

The presence of NBOs in the Raman spectra and dangling bonds in the ESR results indicate that bond breaking during deformation occurs in different forms, such as heterolysis (forming NBO) and homolysis (forming dangling bond). It should be noted that heterolysis requires not only strain but also charge compensation, i.e., a positive charge. However, at least qualitatively, heterolysis appears to be more dominant in this glass under ambient conditions, as it is typically energetically more favorable than homolysis.

Structural modification in local and medium-range order

High-energy X-ray total scattering measurements were performed on glass deformed to a strain of γ ≈ 4 (density ≈ 2.80 g cm⁻³), based on the density–strain relationship,²¹ and the structure factor, S(Q), was obtained (Fig. 8). A first sharp diffraction peak (FSDP), associated with the medium-range structure of the glass network,⁴³ was observed at around 1.8 Å⁻¹ in the structure factor. Upon deformation, the FSDP shifted to higher scattering vectors, reaching approximately 2 Å⁻¹, reflecting a shortening of the medium-range order. From the FSDP position, the real-space distance (d = 2π/Q_FSDP) was estimated to be approximately 3.4 Å. This distance is roughly twice the T–O bond length determined in this study (see below), suggesting that the FSDP predominantly reflects structural periodicities associated with relatively short-range features, such as small rings composed of three- or four-membered TO₄ tetrahedra. Previous studies on aluminosilicate glasses have reported that ring structures of this size produce scattering peaks around 2 Å⁻¹.⁴⁴ Therefore, the observed FSDP likely corresponds to the periodicity of these relatively small rings. That is consistent with the observation from the Raman spectra, intensification of D2 band. Furthermore, the FSDP of the deformed glass was clearly broadened compared to that of the as-made sample. This broadening implies a decrease in the periodicity of the medium-range order caused by shear deformation, resulting in the formation of diverse structural units, including small and/or large distorted rings. These observations are consistent with the broadening of the T–O–T bond angle distribution inferred from the Raman spectra.

Fig. 8 Structure factor of as-made and deformed (γ ≈ 4) glasses. Black and red lines indicate raw and smoothed data. The sharp peak at 1.8–2.0 Å⁻¹ is the first sharp diffraction peak (FSDP).

The total correlation function, T(r), was obtained by Fourier transforming the structure factor (Fig. 9). Based on the ionic radii reported by Shannon and Prewitt,⁴⁵ the correlations observed at approximately 1.6 Å and 2.7 Å can be assigned to T–O and O–O atomic correlations, respectively. The correlation at about 2.0 Å corresponds to Mg–O and ^[VI]Al–O (r = 1.9 Å) atomic pairs,⁴⁵ while the peak at 3.2 Å is attributed to T–T correlations.

Fig. 9 Total correlation function of as-made and deformed (γ ≈ 4) glasses. T in the figure indicates Si and/or Al atom.

In the deformed samples, an increase in intensity was observed in the 1.8–2.0 Å region, consistent with the XANES results, strongly suggesting an increase in the Al coordination number. Mg XANES spectra showed negligible changes in Mg coordination upon deformation (Fig. S4⁴⁶), indicating that the observed changes in this region are primarily due to alterations in Al coordination. The peak at 3.2 Å, corresponding to T–T correlations, exhibited broadening associated with deformation. Raman spectra revealed a widening of the T–O–T bond angle distribution, consistent with the observed changes in T(r). These results suggest that shear deformation induces an increase in the distribution of ring sizes and distortions in the connections between tetrahedral units, leading to the formation of strained ring structures.

Structural anisotropy

In the shear-deformed samples, the two-dimensional X-ray diffraction patterns (halo patterns) exhibited distortion, i.e., the FSDP position showed azimuthal dependence (Fig. 10a). The azimuthal angles corresponding to the maximum Q_FSDP were 37° and 23° for γ = 0.9 and 3.9, respectively. These angles differ from both the orientation of the maximum principal stress (σ₃ = 90°) and the shear stress directions (τ = 135° and its orthogonal 45°). If the deformation were purely uniaxial, the maximum Q_FSDP would be expected along the maximum principal stress direction (“uniaxial comp.” in Fig. 10a). These observations indicate that, at all strain levels, the glass deformed under a stress state distinct from simple uniaxial or simple shear stress.

Fig. 10 (a) Dependence of the FSDP position (Q and d value) on the azimuthal angle. σ₁ and σ₃ indicate the maximum and minimum principal stress directions, respectively, and τ indicates the shear plane direction. The curves represent fits to the experimental data using a cosine function. A potential error of approximately ±10° is included in the azimuthal angle. The dashed line represents the schematic curvature expected under simple uniaxial compression. The apparent distortion of the halo ring in the as made glass (curvature of the plot) is due to the flattening process of the curved imaging plate. (b) Schematic illustration of the relationship between the azimuthal angle and the stress directions. Note that the pistons were removed prior to the X ray scattering measurements.

The magnitude of the azimuthal dependence of Q, defined as the difference between the maximum and minimum Q values (ΔQ), was observed to increase with increasing shear strain (Fig. 11a). ΔQ reached a maximum at γ ≈ 2 and remained nearly constant in the visco-plastic flow regime (γ > 2). Similarly, Q_min shifted toward higher Q values up to γ ≈ 2 but showed little change with further strain evolution (Fig. 11b). In the visco-plastic flow regime, unlike in the densification regime (γ < 1), significant deformation occurred without accompanying changes in medium-range structural order. To investigate anisotropy on the shear plane, a scattering pattern was measured for the γ = 3.9 sample with the X-ray beam incident perpendicular to the shear plane. The results showed almost no azimuthal dependence of the Q value (Fig. 11a, open symbols). In this measurement geometry, all azimuthal angles correspond to directions within the shear plane. The lack of significant azimuthal dependence indicates that there are no notable structural differences on the shear plane (i.e., between the flow direction and the perpendicular direction).

Fig. 11 Change in structural anisotropy (a) and FSDP position (b) of deformed glasses in 2-D X-ray total scattering. All ΔQ data have been corrected by subtracting the anisotropy observed in the as-made sample to account for an artifact on data processing (see Fig. 10). Open symbols were collected using different incident beam direction, which was perpendicular to the shear plane, thus both maximum and minimum directions were placed on the shear plane.

Deformation mechanisms in magnesium aluminosilicate glass

In this study, the glass was observed to deform through multiple modes. In the region where γ < 1, plastic deformation accompanied by densification occurred. In the region where γ > 2, time-dependent visco-plastic flow was observed. In the following sections, the structural origins of these distinct behaviors were discussed.

γ < 1: shear-induced densification

In the low-strain region (γ < 1), densification due to quasi-uniaxial compression is significant. One mechanism contributing to this densification is the increase in three-membered ring structures, which has been frequently reported in experiments under hydrostatic pressure. However, the pronounced azimuthal dependence of the FSDP position observed in the 2D X-ray total scattering measurements indicates that densification occurs concurrently with structural anisotropy. This observation suggests that anisotropy in the glass does not arise solely from large-scale flow but can also result from shear-stress-induced densification. Another possible mechanism for densification is the formation of higher-coordinated Al. While higher Al coordination has been reported at higher pressures under hydrostatic and room-temperature conditions (e.g., ref. 24), its occurrence at such low pressures is characteristic of shear-induced deformation. These shear-specific structural changes promote pronounced densification. Nevertheless, in this low-strain regime, the glass remains “stiff”, allowing significant structural distortion to develop. This is evidenced by the residual stress observed along the compression (principal stress) axis. Moreover, near γ ≈ 1, the formation of dangling bonds (E′ centers) becomes apparent. The creation of these dangling bonds likely results from bond rearrangements, such as the formation of three-membered rings and the increase in Al coordination. The observed dangling bond concentration (≈10¹⁶ spins g⁻¹) is extremely low compared to the total number of Si–O bonds in the glass. For example, in this glass (molar mass ≈64 g mol⁻¹), there are on the order of 10²¹ SiO₄ tetrahedra per gram, making the number of defects five orders of magnitude smaller. Most broken bonds likely recombine, leaving network rearrangements as the primary structural trace. Such bond rearrangements (e.g., higher Al coordination) and significantly distorted bonds may act as precursors to flow when higher strains are subsequently applied.

γ > 1: visco-plastic flow

Up to γ ≈ 1, highly coordinated Al formed, and its coordination number decreased as strain increased. This indicates that Al coordination dynamically evolves during shear deformation and may facilitate shear flow. The increased bond ionicity of Al–O resulting from the coordination increase renders the Al polyhedra and the aluminosilicate network more flexible. Moreover, pressure-induced coordination changes lead to an increase in Al–O bond length. In aluminosilicate melts, this leads to improved O²⁻ diffusivity.²⁹ Indeed, studies on aluminosilicate melts have shown that such highly coordinated Al reduces melt viscosity (e.g., under high pressure¹⁰ and at ambient pressure¹¹). The increase in Al coordination should improve the deformability of the glass in the same manner as aluminosilicate melt studies.

Our result, which include the formation and decomposition of highly-coordinated Al, suggest another possible hypothesis that non-bridging oxygen (NBO) migration facilitated by highly coordinated Al similarly contributes to deformation as shown in Fig. 12(a). The previously presented activation process, involving the consumption of five-coordinated Si during flow in the MD simulation of amorphous SiO₂,⁴⁷ shows good agreement with our result and flow model. In the flow regime, this Al-induced network reorganization appears to play a key role. Notably, the highly coordinated Al observed here was measured after decompression, implying that even higher concentrations existed during deformation and may act as an activation step of deformation process.

Fig. 12 Schematic illustration of atomic scale deformation mechanisms in Mg–aluminosilicate glass. (a) NBO transfer via the formation of highly coordinated Al, (b) bond switching via the formation of dangling bonds (marked with a star). All the Si and Al atoms have a bond to another atom located on the backside of the page. Mg atoms compensate negative charge of NBO or ^[IV]Al outside the figure. The labeled numbers around atom are guides to the eye.

The Mg–aluminosilicate glass studied here not only forms higher-coordinated Al during deformation but also contains such species in the as-made glass. Glasses with preexisting higher-coordinated Al are more prone to forming additional high-coordination species under pressure,^9,48 whereas glasses composed entirely of four-fold coordinated Al, such as jadeite (NaAlSi₂O₆) glass, resist pressure-induced coordination changes.⁴⁸ Several studies report that both initial average CN and pressure-induced coordination number increase strongly depends on cation field strength.^9,49,50 For flow mechanisms involving the consumption of higher-coordinated Al (Fig. 12a), both the initial content and the glass's propensity to form these species are expected to strongly influence deformability. Indeed, Mg–aluminosilicate glass, which has high cation field strength, has been shown to deform more readily than Na-aluminosilicate glass,²¹ highlighting the crucial role of higher-coordinated Al in deformation.

The broadening of the main Raman band and the T–T correlation peak in the total correlation function indicates a widened T–O–T bond angle distribution, revealing the presence of high-energy bonds in the deformed glass. Theoretical calculations show that the potential energy of Si–O–Si linkages rises sharply at narrow bond angles.^51,52 These high-energy bonds may break to form dangling bonds, whose subsequent motion under shear stress could facilitate glass flow (Fig. 12b). The observed FSDP anisotropy, which reflects shorter-range ordering perpendicular to the shear plane, supports the formation of smaller T–O–T bond angles. Although the formation energy of dangling bonds is high and their concentration in the recovered glass is five orders of magnitude lower than that of Si ions, their dynamic formation and annihilation during deformation may still represent a key mechanism contributing to flow.

In samples with shear strain γ > 2, flow-induced deformation with pronounced strain localization was observed. Similar phenomena have been reported in indentation experiments, where they are referred to as “slip lines”⁵³ or “shear bands”.⁵⁴ Such localization indicates that glass deformation is not homogeneous but concentrates at structural weak points. One plausible explanation is preferential deformation in regions where bond rearrangement is frequent, likely associated with domains enriched in flexible structural units (e.g., highly coordinated Al) or distorted rings, including three-membered and other strained configurations (Fig. 12). Consistent with these observations, molecular dynamics simulations of silica glass under shear stress have shown that local deformation arises from structural heterogeneity of the glass network, whereas homogeneous glasses produced by high-pressure treatment do not exhibit such localization.¹³ These findings clearly indicate that eliminating structural heterogeneity through high-pressure treatment strongly influences the deformation mode of glasses. For instance, under confining pressures higher than those applied in the present study, the glass may exhibit uniform deformation with large strains rather than localized flow.

Conclusion

Shear deformation of aluminosilicate glass under confining pressure occurs through two primary modes: densification and visco-plastic flow. Densification predominates at shear strains γ < 1, where deformation proceeds under stress states resembling uniaxial compression. In this regime, densification of up to 5% is accompanied by the formation of highly coordinated Al species, bond distortions detectable as birefringence, creation of three-membered ring structures via bond rearrangements, and the emergence of dangling bonds as structural traces.

In contrast, visco-plastic flow dominates at γ > 2, likely triggered by unstable, highly strained bonds formed in the low-strain regime and by increased ionicity of bonds associated with highly coordinated Al. The primary flow mechanism involves non-bridging oxygen transfer facilitated by dynamic Al coordination changes (e.g., ^[VI]Al → ^[V]Al → ^[IV]Al). Such cooperative local rearrangements enhance flow over medium- to long-range scales, effectively dissipating stress. These stress-induced structural transformations are thus a key factor underpinning the remarkable fracture toughness of this glass, demonstrating how microscopic structural dynamics govern macroscopic mechanical resilience.

Conflicts of interest

There are no conflicts to declare.

Data availability

The X-ray absorption data, associated analysis results and experimental details supporting this article have been included within the article and the supplementary information (SI). The supplementary information includes the X-ray absorption data, associated analysis results, and experimental details supporting this article. See DOI: https://doi.org/10.1039/d5cp03427b.

Acknowledgements

Authors thank Prof. Hiroshi Kondoh, the editor in this journal, and two anonymous reviewers very much for their careful handling and insightful comments, which greatly improved the clarity of our manuscript. The glass samples used in this study were provided by Nippon Electric Glass Co., Ltd. This work was supported by the Joint Usage/Research Center PRIUS, Ehime University, Japan (2017-A16, 2018-A15, 2019-A45). T. O. provided valuable advice on sample fabrication and deformation experiments. High-energy X-ray total scattering (HEXTS) measurements were conducted as preliminary experiments under proposals 2022B1207, 2023B1115 and 2023B1116, approved by JASRI, SPring-8. Al and Mg K-edge XANES measurements were performed with the approval of the Scientific Review Committee at the SR Center, Ritsumeikan University (S18025), with valuable advice from M. Y. This work was partially supported by a Grant-in-Aid for Scientific Research C (25400517, 23K04893) awarded to A. Y., and also funded by Nippon Electric Glass Co., Ltd.

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Footnotes

† Present address: Faculty of Materials for Energy, Shimane University, 1060 Nishikawatsu-cho, Matsue 690-8504, Japan.

‡ Present address: AGC Inc., 1-1, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan.

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