HIGH FRACTURE TOUGHNESS GLASSES WITH HIGH CENTRAL TENSION

BACKGROUND
Field

The present specification generally relates to glass-based articles exhibiting improved damage resistance and, more particularly, to glass and glass ceramic articles having high fracture toughness and high central tension and that may be strengthened by ion exchange.

Technical Background

Glass is used in a variety of products having a high likelihood of sustaining damage, such as in portable electronic devices, touch screens, scanners, sensors, LIDAR equipment, and architectural materials. Glass breakage is common in these applications.

Accordingly, a need exists for alternative compositions that are more resistant to breakage.

SUMMARY

According to a first aspect A1, a glass-based article includes a first surface and a second surface opposing the first surface defining a thickness (t) and is formed from a composition. The composition comprises: from greater than or equal to 48 mole % to less than or equal to 75 mole % SiO₂; from greater than or equal to 8 mole % to less than or equal to 40 mole % Al₂O₃; from greater than or equal to 9 mole % to less than or equal to 40 mole % Li₂O; from greater than 0 mole % to less than or equal to 3.5 mole % Na₂O; from greater than or equal to 9 mole % to less than or equal to 28 mole % R₂O, wherein R is an alkali metal and the R₂O comprises at least Li₂O and Na₂O; from greater than or equal to 0 mole % to less than or equal to 10 mole % Ta₂O₅; from greater than or equal to 0 mole % to less than or equal to 4 mole % ZrO₂; from greater than or equal to 0 mole % to less than or equal to 4 mole % TiO₂; from greater than or equal to 0 mole % to less than or equal to 3 mole % ZnO; from greater than or equal to 0 mole % to less than or equal to 3.5 mole % R′O, where R′ is a metal selected from Ca, Mg, Sr, Ba, Zn, and combinations thereof; and from greater than or equal to 0 mole % to less than or equal to 8 mole % RE₂O₃, where RE is a rare earth metal selected from Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and combinations thereof. The glass is ion exchangeable for strengthening. R₂O++R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂is in a range from greater than or equal to −8 mole % to less than or equal to 5 mole %. ZrO₂+TiO₂+SnO₂is in a range from greater than or equal to 0 mol % to less than or equal to 2 mole %. The composition is free of As₂O₃, Sb₂O₃, and PbO

A second aspect A2 includes the glass-based article according to the first aspect A1, wherein the glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression, and a tensile stress region extending from the depth of compression toward the second surface, the tensile stress region having a maximum central tension greater than or equal to 175 MPa.

A third aspect A3 includes the glass-based article according to any of the foregoing aspects, wherein the tensile stress region has a maximum central tension from greater than or equal to 175 MPa to less than or equal to 600 MPa.

A fourth aspect A4 includes the glass-based article according to any of the foregoing aspects, further comprising a fracture toughness of greater than 0.7 MPa√m.

A fifth aspect A5 includes the glass-based article of any of the foregoing aspects, further comprising a critical strain energy release rate of greater than 7 J/m².

A sixth aspect A6 includes the glass-based article of any of the foregoing aspects further comprising a Young's modulus of greater than 70 GPa.

A seventh aspect A7 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 10 mole % of the Ta₂O₅.

An eighth aspect A8 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 8 mole % of the RE₂O₃.

A ninth aspect A9 includes the glass-based article of any of the foregoing aspects, wherein RE₂O₃is selected from Y₂O₃, La₂O₃, and combinations thereof, and wherein the glass-based article comprises from greater than or equal to 0 mole % to less than or equal to 7 mole % of the Y₂O₃and from greater than or equal to 0 mole % to less than or equal to 5 mole % of the La₂O₃.

A tenth aspect A10 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 4 mole % of the TiO₂.

An eleventh aspect A11 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 4 mole % of the ZrO₂.

A twelfth aspect A12 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 3.5 mole % of the R′O.

A thirteenth aspect A13 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 3 mole % MgO.

A fourteenth aspect A14 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 3 mole % CaO.

A fifteenth aspect A15 includes the glass-based article of any of the foregoing aspects, comprising from greater than or equal to 50 mole % to less than or equal to 64 mole % of the SiO₂.

A sixteenth aspect A16 includes the glass-based article of any of the foregoing aspects, comprising from greater than or equal to 16 mole % to less than or equal to 24 mole % of the Al₂O₃.

A seventeenth aspect A17 includes the glass-based article of any of the foregoing aspects, comprising from greater than or equal to 12 mole % to less than or equal to 18 mole % of the R₂O.

An eighteenth aspect A18 includes the glass-based article of any of the foregoing aspects, wherein R₂O further comprises K₂O.

A nineteenth aspect A19 includes the glass-based article of any of the foregoing aspects, comprising from greater than 0 mole % to less than or equal to 3 mole % of the K₂O.

A twentieth aspect A20 includes the glass-based article of any of the foregoing aspects, wherein R₂O−Al₂O₃−Ta₂O₅is in a range from greater than or equal to −12 mole % to less than or equal to 6 mole %.

A twenty-first aspect A21 includes the glass-based article of any of the foregoing aspects, wherein R₂O+R′O−Al₂O₃−Ta₂O₅is in a range from greater than or equal to −7 mole % to less than or equal to 9 mole %.

A twenty-second aspect A22 includes the glass-based article of any of the foregoing aspects, wherein Li₂O/R₂O is in a range from greater than or equal to 0.5 to less than or equal to 1.

A twenty-third aspect A23 includes the glass-based article of any of the foregoing aspects, wherein Li₂O/(Al₂O₃+Ta₂O₅) is in a range from greater than or equal to 0.4 to less than or equal to 1.5.

A twenty-fourth aspect A24 includes the glass-based article of any of the foregoing aspects, further comprising from greater than or equal to 0 mole % to less than or equal to 7 mole % B₂O₃.

A twenty-fifth aspect A25 includes the glass-based article of any of the foregoing aspects, further comprising from greater than or equal to 0 mole % to less than or equal to 5 mole % P₂O₅.

A twenty-sixth aspect A26 includes the glass-based article of any of the foregoing aspects, further comprising: from greater than or equal to 0 mole % to less than or equal to 3 mole % MgO; from greater than or equal to 0 mole % to less than or equal to 3 mole % CaO; from greater than or equal to 0 mole % to less than or equal to 3 mole % SrO; and from greater than or equal to 0 mole % and less than or equal to 3 mole % BaO.

A twenty-seventh aspect A27 includes the glass-based article of any of the foregoing aspects, wherein the glass-based article is strengthened by ion exchange and the glass-based article comprises a stored strain energy greater than or equal to 20 J/m².

A twenty-eigth aspect A28 includes the glass-based article of any of the foregoing aspects, wherein the glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression, and a tensile stress region extending from the depth of compression toward the second surface, the tensile stress region having a maximum central tension greater than or equal to 175 MPa and the glass-based article comprising a critical strain energy release rate greater than or equal to 7 J/m².

A twenty-ninth aspect A29 includes the glass-based article of any of the foregoing aspects, wherein a value of an arithmetic product of the critical strain energy release rate and the maximum central tension is greater than or equal to 2000 MPa·J/m².

A thirtieth aspect A30 includes the glass-based article of any of the foregoing aspects, wherein the glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression, and a tensile stress region extending from the depth of compression toward the second surface, the tensile stress region having a maximum central tension greater than or equal to 175 MPa and the glass-based article comprising a fracture toughness of greater than 0.7 MPa√m.

A thirty-first aspect A31 includes the glass-based article of any of the foregoing aspects, wherein a value of an arithmetic product of the fracture toughness and the central tension is greater than or equal to 200 MPa²√m.

A thirty-second aspect A32 includes the glass-based article of any of the foregoing aspects, wherein the glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression, and a tensile stress region extending from the depth of compression toward the second surface, the tensile stress region having a maximum central tension greater than or equal to 175 MPa and the glass-based article comprising at least one strengthening ion having a diffusivity into the glass-based article at 430° C. with units micrometers²/hour, a value of an arithmetic product of the central tension and the diffusivity is greater than or equal to 50,000 MPa micrometers²/hour.

A thirty-third aspect A33 includes a glass-based article comprising a composition comprising SiO₂, Li₂O, Ta₂O₅, and Al₂O₃, the Al₂O₃content being greater than or equal to 12 mole %. The glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression, and a tensile stress region extending from the depth of compression toward a second surface opposite the first surface, the tensile stress region having a maximum central tension greater than or equal to 160 MPa.

A thirty-fourth aspect A34 includes the glass-based article of the thirty-third aspect A33, wherein the Al₂O₃content is greater than or equal to 14 mole % of the composition.

A thirty-fifth aspect A35 includes the glass-based article of the thirty-third aspect A33 or the thirty-fourth aspect A34, wherein the Al₂O₃content is greater than or equal to 16 mole % of the composition.

Additional features and advantages of the glass articles described herein will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments described herein, including the detailed description which follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description and the following detailed description describe various embodiments and are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments, and are incorporated into and constitute a part of this specification. The drawings illustrate the various embodiments described herein, and together with the description serve to explain the principles and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is cross-sectional view of an exemplary ion exchanged glass article in accordance with embodiments described herein;

FIG. 1B is a stress profile of a glass article through a cross-section as a function of depth from the surface in accordance with embodiments described herein;

FIG. 2 is a graph comparing drop performance of embodiments disclosed herein to drop performance of other glass-based articles;

FIG. 3 is a graph comparing maximum central tension attained in glass-based articles according to embodiments described herein having yittria (Y₂O₃) versus embodiments not including Y₂O₃;

FIG. 4 graphically depicts experimental fracture toughness and critical strain energy release rate values as as a function of Y₂O₃content;

FIG. 5 is a graph comparing drop performance of embodiments disclosed herein to drop performance of other glass-based articles;

FIG. 6 is a graph showing repeated drop to failure survival as a function of central tension for 0.8 mm thick glass-based articles in accordance with embodiments described herein;

FIG. 7 is a graph showing the effect of replacing Li₂O and Na₂O through ion exchange on K_1Cand Young's modulus in accordance with embodiments described herein; and

FIG. 8 is a graph showing the stress profile through the thickness of a 1 mm-thick glass-based article in accordance with embodiments described herein.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments of glass-based articles having high fracture toughness and high central tension that may be strengthened by ion exchange. According to one embodiment, a glass-based article includes a first surface and a second surface opposing the first surface defining a thickness (t) and is formed from a composition. The composition comprises: from greater than or equal to 48 mole % to less than or equal to 75 mole % SiO₂; from greater than or equal to 8 mole % to less than or equal to 40 mole % Al₂O₃; from greater than or equal to 9 mole % to less than or equal to 40 mole % Li₂O; from greater than to 0 mole % to less than or equal to 3.5 mole % Na₂O; from greater than or equal to 9 mole % to less than or equal to 28 mole % R₂O, wherein R is an alkali metal and the R₂O comprises at least Li₂O and Na₂O; from greater than or equal to 0 mole % to less than or equal to 10 mole % Ta₂O₅; from greater than or equal to 0 mole % to less than or equal to 4 mole % ZrO₂; from greater than or equal to 0 mole % to less than or equal to 4 mole % TiO₂; from greater than or equal to 0 mole % to less than or equal to 3 mole %; from greater than or equal to 0 mole % to less than or equal to 3.5 mole % R′O, where R′ is an alkaline earth metal selected from Ca, Mg, Zn, and combinations thereof; and from greater than or equal to 0 mole % to less than or equal to 8 mole % RE₂O₃, where RE is a rare earth metal selected from Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and combinations thereof. The glass is ion exchangeable for strengthening. The sum of R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂is in a range from greater than or equal to −8 to less than or equal to 5. ZrO₂+TiO₂+SnO₂is in a range from greater than or equal to 0 mol % to less than or equal to 2 mole %. The composition is free of As₂O₃, Sb₂O₃, and PbO. Various embodiments of glass-based articles and the properties thereof will be described herein with specific reference to the appended drawings.

As used herein, the terms “glass-based article” and “glass-based substrates” are used in their broadest sense to include any object made wholly or partly of glass and/or glass ceramic. Glass-based articles include laminates of glass and non-glass materials, laminates of glass and polymers, laminates of glass and crystalline materials, and glass-ceramics (including an amorphous phase and a crystalline phase).

In the embodiments of the compositions described herein, the concentrations of constituent components (e.g., SiO₂, Al₂O₃, and the like) are specified in mole percent (mol. %) on an oxide basis, unless otherwise specified.

The terms “free” and “substantially free,” when used to describe the concentration and/or absence of a particular constituent component in a composition, means that the constituent component is not intentionally added to the composition. However, the composition may contain traces of the constituent component as a contaminant or tramp in amounts of less than 0.05 mol. %.

The glass-based articles described herein may be chemically strengthened by, for example, ion exchange and may exhibit stress profiles that are distinguished from those exhibited by known strengthened glass articles. In this disclosure glass-based substrates are unstrengthened and glass-based articles refer to glass-based substrates that have been strengthened (by, for example, ion exchange). In this process, ions at or near the surface of the glass-based article are replaced by—or exchanged with—larger ions having the same valence or oxidation state at a temperature below the glass transition temperature. Without intending to be bound by any particular theory, it is believed that in those embodiments in which the glass-based article comprises an alkali aluminosilicate glass, ions in the surface layer of the glass and the larger ions are monovalent alkali metal cations, such as Li⁺ (when present in the glass-based article), Na⁺, K⁺, Rb⁺, and Cs⁺. Alternatively, monovalent cations in the surface layer may be replaced with monovalent cations other than alkali metal cations, such as Ag⁺ or the like. In such embodiments, the monovalent ions (or cations) exchanged into the glass-based substrate generate a stress in the resulting glass-based article.

A cross-section view of an exemplary ion exchanged glass article 200 is shown in FIG. 1A and typical stress profile obtained by ion exchange is shown in FIG. 1B. The ion exchanged glass article 200 includes a first surface 201A, a second surface 201B, and a thickness ti between the first surface 201A and the second surface 201B. In some embodiments, the ion exchanged glass article 200 may exhibit a compressive stress, as that term is defined below, that decreases from the first surface 201A to a depth of compression 230A, as that term is defined below, until it reaches a region of central tension 220 having a maximum central tension. Accordingly, in some embodiments, the region of central tension 220 extends from the depth of compression 230A towards the second surface 201B of the glass article 200. Likewise, the ion exchanged glass article 200 exhibits a compressive stress 210B that decreases from the second surface 201B to a depth of compression 230B until it reaches a region of central tension 220 having a maximum central tension. Accordingly, the region of central tension 220 extends from the depth of compression 230B towards the first surface 201A such that the region of central tension 220 is disposed between the depth of compression 230B and the depth of compression 230A. The stress profile in the ion exchanged glass article 200 may have various configurations. For example and without limitation, the stress profile may be similar to an error function, such as the stress profile depicted in FIG. 1B. However, it should be understood that other shapes are contemplated and possible, including parabolic stress profiles (e.g., as depicted in FIG. 8) or the like.

Ion exchange processes are typically carried out by immersing a glass-based substrate in a molten salt bath (or two or more molten salt baths) containing the larger ions to be exchanged with the smaller ions in the glass-based substrate. It should be noted that aqueous salt baths may also be utilized. In addition, the composition of the bath(s) may include more than one type of larger ion (e.g., Na+ and K+) or a single larger ion. It will be appreciated by those skilled in the art that parameters for the ion exchange process, including, but not limited to, bath composition and temperature, immersion time, the number of immersions of the glass-based article in a salt bath (or baths), use of multiple salt baths, additional steps such as annealing, washing, and the like, are generally determined by the composition of the glass-based article (including the structure of the article and any crystalline phases present) and the desired depth of compression and compressive stress, as those terms are defined below, of the glass-based article that results from strengthening. By way of example, ion exchange of glass-based substrates may be achieved by immersion of the glass-based substrates in at least one molten bath containing a salt such as, but not limited to, nitrates, sulfates, and chlorides of the larger alkali metal ion. Typical nitrates include KNO₃, NaNO₃, LiNO₃, and combinations thereof. In one or more embodiments, NaSO₄may be used, as well, with or without a nitrate. The temperature of the molten salt bath typically is in a range from about 370° C. up to about 480° C., while immersion times range from about 15 minutes up to about 100 hours depending on glass thickness, bath temperature and glass (or monovalent ion) diffusivity. However, temperatures and immersion times different from those described above may also be used.

In one or more embodiments, the glass-based substrates may be immersed in a molten salt bath of 100% NaNO₃having a temperature from about 370° C. to about 480° C. In some embodiments, the glass-based substrate may be immersed in a molten mixed salt bath including from about 5% to about 90% KNO₃and from about 10% to about 95% NaNO₃. In some embodiments, the glass-based substrate may be immersed in a molten mixed salt bath including Na₂SO₄and NaNO₃and have a wider temperature range (e.g., up to about 500° C.). In one or more embodiments, the glass-based article may be immersed in a second bath, after immersion in a first bath. Immersion in a second bath may include immersion in a molten salt bath including 100% KNO₃for 15 minutes to 8 hours.

In one or more embodiments, the glass-based substrate may be immersed in a molten, mixed salt bath including NaNO₃and KNO₃(e.g., 49%/51%, 50%/50%, 51%/49%) having a temperature less than about 420° C. (e.g., about 400° C. or about 380° C.) for less than about 5 hours, or even about 4 hours or less.

Ion exchange conditions can be tailored to provide a “spike” or to increase the slope of the stress profile at or near the surface of the resulting glass-based article. This spike can be achieved by a single ion-exchange bath or multiple baths, with the bath(s) having a single composition or mixed composition, due to the unique properties of the glass compositions used in the glass-based articles described herein.

As used herein, “DOC” or “depth of compression” refers to the depth at which the stress within the glass-based article changes from compressive to tensile stress. At the DOC, the stress changes from a negative (compressive) stress to a positive (tensile) stress.

As used herein, the terms “chemical depth,” “chemical depth of layer,” and “depth of chemical layer” may be used interchangeably and refer to the depth at which an ion of the metal oxide or alkali metal oxide (e.g., the metal ion or alkali metal ion) diffuses into the glass-based article and the depth at which the concentration of the ion reaches a minimum value, as determined by Electron Probe Micro-Analysis (EPMA) or Glow Discharge-Optical Emission Spectroscopy (GD-OES). In particular, the depth of Na₂O diffusion or Na+ ion concentration or the depth of K₂O diffusion or K+ ion concentration may be determined using EPMA or GD-OES.

According to the convention normally used in the art, compression is expressed as a negative (<0) stress and tension is expressed as a positive (>0) stress, unless specifically noted otherwise. Throughout this description, however, when speaking in terms of compressive stress CS, such is given without regard to positive or negative values—i.e., as recited herein, CS=|CS|.

CS is measured with a surface stress meter (FSM) using commercially available instruments such as the FSM-6000, manufactured by Orihara Industrial Co., Ltd. (Japan). Surface stress measurements rely upon the measurement of the stress optical coefficient (SOC), which is related to the birefringence of the glass. SOC may be measured using the disc method according to ASTM standard C770-16 (2016), entitled “Standard Test Method for Measurement of Glass Stress-Optical Coefficient,” the contents of which are incorporated herein by reference in their entirety. The modification includes using a glass disc as the specimen with a thickness of 5 to 10 mm and a diameter of 12.7 mm, wherein the disc is isotropic and homogeneous and core drilled with both faces polished and parallel.

DOC and maximum central tension (or “maximum CT”) values are measured using either a refracted near-field (RNF) method or a scattered light polariscope (SCALP). Either may be used to measure the stress profile. When the RNF method is utilized, the maximum CT value provided by SCALP is utilized. In particular, the stress profile measured by RNF is force balanced and calibrated to the maximum CT value provided by a SCALP measurement. The RNF method is described in U.S. Pat. No. 8,854,623, entitled “Systems and methods for measuring a profile characteristic of a glass sample,” which is incorporated herein by reference in its entirety. In particular, the RNF method includes placing the glass-based article adjacent to a reference block, generating a polarization-switched light beam that is switched between orthogonal polarizations at a rate of between 1 Hz and 50 Hz, measuring an amount of power in the polarization-switched light beam and generating a polarization-switched reference signal, wherein the measured amounts of power in each of the orthogonal polarizations are within 50% of each other. The method further includes transmitting the polarization-switched light beam through the glass sample and reference block for different depths into the glass sample, then relaying the transmitted polarization-switched light beam to a signal photodetector using a relay optical system, with the signal photodetector generating a polarization-switched detector signal. The method also includes dividing the detector signal by the reference signal to form a normalized detector signal and determining the profile characteristic of the glass sample from the normalized detector signal. The RNF profile is then smoothed. As noted above, the FSM technique is used for the surface CS and slope of the stress profile in the CS region near the surface.

The fracture toughness Kic value recited in this disclosure refers to a value as measured by chevron notched short bar (CNSB) method disclosed in Reddy, K. P. R. et al, “Fracture Toughness Measurement of Glass and Ceramic Materials Using Chevron-Notched Specimens,” J. Am. Ceram. Soc., 71 [6], C-310-C-313 (1988) except that Y*_mis calculated using equation 5 of Bubsey, R. T. et al., “Closed-Form Expressions for Crack-Mouth Displacement and Stress Intensity Factors for Chevron-Notched Short Bar and Short Rod Specimens Based on Experimental Compliance Measurements,” NASA Technical Memorandum 83796, pp. 1-30 (October 1992).

Density is determined by the buoyancy method according to ASTM C693-93 (2019).

Young's modulus E, Poisson's ratio, and shear modulus values recited in this disclosure refer to values measured by a resonant ultrasonic spectroscopy technique as set forth in ASTM C623-92 (2015), titled “Standard Test Method for Young's Modulus, Shear Modulus, and Poisson's Ratio for Glass and Glass-Ceramics.”

As used herein, the term “specific modulus” means the value of the Young's modulus divided by the density.

As used herein, the term “Poisson's ratio” means the ratio of the proportional decrease in a lateral measurement to the proportional increase in length in a sample of a glass-based article, as described herein, which is elastically stretched.

The stored strain energy Σ₀may be calculated according to the following equation (I):

$\begin{matrix} Σ_{0} = \frac{1 - v}{E_{m o d}} \int_{- z^{*}}^{+ z^{*}} σ^{2} d z & (I) \end{matrix}$

where ν is Poisson's ratio, E_modis Young's modulus (in MPa), σ is stress (in MPa), z*=0.5t′, z being the depth and t′ being the thickness (in micrometers) of the tensile region only (i.e., the thickness of the region between the depth of compression 230A and the depth of compression 230B in FIG. 1B).

Critical strain energy release rate G_1Cwas calculated according to the following equation (II):

$\begin{matrix} G_{1 C} = \frac{K_{1 C}^{2}}{E} & (II) \end{matrix}$

where K_1Cis the fracture toughness and E is the Young's modulus. G_1Cis conventionally reported in units of J/m².

Coefficients of thermal expansion (CTE) are expressed in terms of 10⁻⁷1° C. and represent the average value measured over a temperature range from about 20° C. to about 300° C., unless otherwise specified.

The terms “strain point” and “T_strain” as used herein, refer to the temperature at which the viscosity of the glass composition is 3×10^14.7poise.

The term “annealing point,” as used herein, refers to the temperature at which the viscosity of the glass composition is 1×10^13.2poise.

The term “softening point,” as used herein, refers to the temperature at which the viscosity of the glass composition is 1×10^7.6poise.

Strain and annealing points are measured according to the beam bending viscosity method which measures the viscosity of inorganic glass from 10¹²to 10¹⁴poise as a function of temperature in accordance with ASTM C598-93 (2019), titled “Standard Test Method for Annealing Point and Strain Point of Glass by Beam Bending,” which is incorporated herein by reference in its entirety.

The softening point was measured according to the parallel plate viscosity method which measures the viscosity of inorganic glass from 10⁷to 10⁹poise as a function of temperature, similar to the ASTM C1351M-96 (2017), titled “Standard Test Method for Measurement of Viscosity of Glass Between 10⁴Pa·s and 10⁸Pa·s by Viscous Compression of a Solid Right Cylinder,” which is incorporated herein by reference in its entirety.

As used herein, the term “liquidus viscosity” refers to the viscosity of a molten glass at the liquidus temperature, wherein the term “liquidus temperature” refers to the temperature at which crystals first appear as a molten glass cools down from the melting temperature (or the temperature at which the very last crystals melt away as temperature is increased from room temperature). In general, the glass-based articles (or the compositions used to form such articles) described herein have a liquidus viscosity of less than about 100 kilopoise (kP). In some embodiments, the glass-based articles (or the compositions used to form such articles) exhibit a liquidus viscosity of less than about 80 kP, less than about 60 kP, less than about 40 kP, less than about 30 kP, less than about 20 kP, or even less than about 10 kP (e.g., in the range from about 0.5 kP to about 10 kP). The liquidus viscosity is determined by the following method. First the liquidus temperature of the glass is measured in accordance with ASTM C829-81 (2015), titled “Standard Practice for Measurement of Liquidus Temperature of Glass by the Gradient Furnace Method”. Next the viscosity of the glass at the liquidus temperature is measured in accordance with ASTM C965-96(2017), titled “Standard Practice for Measuring Viscosity of Glass Above the Softening Point,” which is incorporated herein by reference in its entirety.

Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

Directional terms as used herein—for example up, down, right, left, front, back, top, bottom—are made only with reference to the figures as drawn and are not intended to imply ab solute orientation.

Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order, nor that with any apparatus specific orientations be required. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or that any apparatus claim does not actually recite an order or orientation to individual components, or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, or that a specific order or orientation to components of an apparatus is not recited, it is in no way intended that an order or orientation be inferred, in any respect. This holds for any possible non-express basis for interpretation, including: matters of logic with respect to arrangement of steps, operational flow, order of components, or orientation of components, plain meaning derived from grammatical organization or punctuation, and the number or type of embodiments described in the specification.

As used herein, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having two or more such components, unless the context clearly indicates otherwise.

Glass articles that survive repeated drops on damaging surfaces are well suited for applications requiring rugged components, such as for touch screens of electronic devices. Some glass substrates or glass articles made with superior resistance to breakage are formed so as to avoid a high number of fragments formed upon breakage. For example, the glass articles may be formed so as to exhibit a fragmentation density of greater than about 5 fragments/cm²of the glass article when subjected to a point impact by an object or a drop onto a solid surface with sufficient force to break the glass article into multiple small pieces. Stored strain energy (SSE) may be an indication of a glass substrate or glass article having a desirable fragmentation pattern For example, glass substrates or glass articles with a stored strain energy greater than about 20 J/m²or even greater than about 24 J/m²may exhibit a fragmentation density of greater than about 5 fragments/cm².

Nonetheless, highly fragmentable glasses may now be used for some applications, such as touch screen mounted on device displays, that have a high likelihood of breakage, because many touchscreens are now directly laminated to the display without an air gap. As such, ejection of particles is less likely due to the lamination. Thus, as more fully described below, highly fragmentable glasses may provide even better drop performance and a more desirable break pattern with fewer ejected particles than non-frangible glasses.

Disclosed herein are glass-based articles comprising glass compositions that mitigate the aforementioned problems. Specifically, the glass compositions enable stress profiles and relatively high central tensions, stored strain energies, fracture toughnesses, and critical strain energy release rates such that the glass-based articles made from the compositions provide enhanced drop performance relative to previously known articles.

In one or more embodiments, SiO₂is the largest constituent of the glass composition and, as such, is the primary constituent of the resulting glass network. That is, SiO₂is the primary glass forming oxide. SiO₂enhances the viscosity (strain, anneal, and softening points, as well as the viscosity at the liquidus temperature) of the glass, which may in turn enhance forming and may also lower the CTE. Accordingly, a high SiO₂concentration is generally desired. However, if the content of SiO₂is too high, the formability of the glass may be diminished as higher concentrations of SiO₂increase the difficulty of melting, softening, and molding the glass which, in turn, adversely impacts the formability of the glass. If the SiO₂content is too high or too low, the liquidus temperature may be increased, which may also reduce formability.

In embodiments, the compositions may include SiO₂in an amount greater than or equal to 48 mol. %. The amount of SiO₂may be less than or equal to 77 mol. %. Accordingly, in embodiments of the compositions, the compositions may comprise SiO₂in an amount greater than or equal to 48 mol. % and less than or equal to 77 mol. %. In embodiments, the lower bound of the amount of SiO₂in the composition may be greater than or equal to 48 mol. %, greater than or equal to 49 mol. %, greater than or equal to 50 mol. %, greater than or equal to 51 mol. %, greater than or equal to 52 mol. %, greater than or equal to 53 mol. %, greater than or equal to 54 mol. %, greater than or equal to 55 mol. %, greater than or equal to 56 mol. %, greater than or equal to 57 mol. %, greater than or equal to 58 mol. %, greater than or equal to 59 mol. %, or even greater than or equal to 60 mol. %. In embodiments, the upper bound of the amount of SiO₂in the composition may be less than or equal to 77 mol. %, less than or equal to 76 mol. %, less than or equal to 75 mol. %, less than or equal to 74 mol. %, less than or equal to 73 mol. %, less than or equal to 72 mol. %, less than or equal to 71 mol. %, less than or equal to 70 mol. %, less than or equal to 69 mol. %, less than or equal to 68 mol. %, less than or equal to 67 mol. %, less than or equal to 66 mol. %, less than or equal to 65 mol. %, less than or equal to 64 mol. %, less than or equal to 63 mol. %, less than or equal to 62 mol. %, or even less than or equal to 61 mol. %. It should be understood that the amount of SiO₂in the compositions may be within a range formed from any one of the lower bounds for SiO₂and any one of the upper bounds of SiO₂described herein.

For example and without limitation, in embodiments, the compositions may include greater than or equal to 48 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 49 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 50 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 51 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 52 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 53 mol. % and less than or equal to 77 mol. % SiO₂. In embodiments, the compositions may include greater than or equal to 48 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 49 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 50 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 51 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 52 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 53 mol. % and less than or equal to 75 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 50 mol. % and less than or equal to 64 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 48 mol. % and less than or equal to 64 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 49 mol. % and less than or equal to 63 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 50 mol. % and less than or equal to 62 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 51 mol. % and less than or equal to 61 mol. % SiO₂. In embodiments, the composition may include greater than or equal to 58 mol. % and less than or equal to 65 mol. % SiO₂.

In one or more embodiments, the compositions include Al₂O₃. Al₂O₃may act as both a conditional network former and a modifier. While not intending to be bound by any particular theory, it is believed that Al₂O₃binds the alkali oxides in the glass network, increasing the viscosity of the glass. Al₂O₃may affect alkali diffusivity, Young's modulus, and fracture toughness of the resultant glass. The ion exchange rate and maximum ion exchange stress may be maximized when the Al₂O₃content is close to the total alkali oxide content. It is also believed that Al₂O₃may contribute to a stable article with low CTE and improved rigidity. However, excessive additions of Al₂O₃to the composition may also increase the softening point of the glass and raise the liquidus temperature, which may adversely impact the formability of the composition.

In embodiments, the compositions may include Al₂O₃in an amount greater than or equal to 5 mol. %. The amount of Al₂O₃may be less than or equal to 28 mol. %. In embodiments, the compositions may include Al₂O₃in an amount greater than or equal to 8 mol. %. The amount of Al₂O₃may be less than or equal to 40 mol. %. If the Al₂O₃content is too low, ion exchange stress, viscosity, and fracture toughness may all be too low. However, if the Al₂O₃content is too high, the liquidus temperature may be too high and the glass may crystallize. Accordingly, in embodiments of the compositions, the compositions may comprise Al₂O₃in an amount greater than or equal to 5 mol. % and less than or equal to 28 mol. %. In embodiments, the compositions may comprise Al₂O₃in an amount greater than or equal to 8 mol. % and less than or equal to 40 mol. %. In embodiments, the lower bound of the amount of Al₂O₃in the composition may be greater than or equal to 5 mol. %, greater than or equal to 6 mol. %, greater than or equal to 7 mol. %, greater than or equal to 8 mol. %, greater than or equal to 9 mol. %, greater than or equal to 10 mol. %, greater than or equal to 11 mol. %, greater than or equal to 12 mol. %, greater than or equal to 13 mol. %, greater than or equal to 14 mol. %, greater than or equal to 15 mol. %, greater than or equal to 16 mol. %, greater than or equal to 17 mol. %, greater than or equal to 18 mol. %, greater than or equal to 19 mol. %, or even greater than or equal to 20 mol. %. In embodiments, the upper bound of the amount of Al₂O₃in the composition may be less than or equal to 40 mol. %, less than or equal to 35 mol. %, less than or equal to 30 mol. %, less than or equal to 28 mol. %, less than or equal to 27 mol. %, less than or equal to 26 mol. %, less than or equal to 25 mol. %, less than or equal to 24 mol. %, less than or equal to 23 mol. %, less than or equal to 22 mol. %, less than or equal to 21 mol. %, less than or equal to 19 mol. %, less than or equal to 18 mol. %, less than or equal to 17 mol. %, or even less than or equal to 16 mol. %. It should be understood that the amount of Al₂O₃in the compositions may be within a range formed from any one of the lower bounds for Al₂O₃and any one of the upper bounds of Al₂O₃described herein.

For example and without limitation, the compositions may include Al₂O₃in an amount greater than or equal to 5 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 5 mol. % and less than or equal to 27 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 5 mol. % and less than or equal to 26 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 5 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 6 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 7 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 8 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 9 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 10 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 10 mol. % and less than or equal to 27 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 16 mol. % and less than or equal to 24 mol. %. In embodiments, the compositions may include Al₂O₃in an amount greater than or equal to 8 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 8 mol. % and less than or equal to 35 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 8 mol. % and less than or equal to 30 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 8 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 9 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 10 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 11 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 12 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Al₂O₃in the composition is greater than or equal to 13 mol. % and less than or equal to 40 mol. %.

The compositions also include one or more alkali oxides. The sum of all alkali oxides (in mol. %) is expressed herein as R₂O. Specifically, R₂O is the sum of Li₂O (mol. %), Na₂O (mol. %), K₂O (mol. %), Rb₂O (mol. %), and Cs₂O (mol. %) present in the composition. Without intending to be bound by any particular theory, it is believed that the alkali oxides aid in decreasing the softening point, thereby offsetting the increase in the softening point of the composition due the amount of SiO₂in the composition. The decrease in the softening point may be further enhanced by including combinations of alkali oxides (e.g., two or more alkali oxides) in the composition, a phenomenon referred to as the “mixed alkali effect.” Additionally, the presence of R₂O may enable chemical strengthening by ion exchange. Because the maximum CT is dependent on the amount of alkali that can be ion exchanged into the glass, in some embodiments, the compositions may have at least 10 mol. % R₂O.

In embodiments, the amount of alkali oxide (i.e., the amount of R₂O) in the compositions may be greater than or equal to 5 mol. % and less than or equal to 28 mol. %. If the R₂O content is too low, there are too few ions to exchange and the resultant stress after ion exchange is too low. If, however, the R₂O content is too high, the glass may become unstable, may devitrify, and may exhibit poor chemical durability. In embodiments, the lower bound of the amount of R₂O in the composition may be greater than or equal to 5 mol. %, greater than or equal to 6 mol. %, greater than or equal to 7 mol. %, greater than or equal to 8 mol. %, greater than or equal to 9 mol. %, greater than or equal to 10 mol. %, greater than or equal to 11 mol. %, greater than or equal to 12 mol. %, greater than or equal to 13 mol. %, greater than or equal to 14 mol. %, greater than or equal to 15 mol. %, or even greater than or equal to 16 mol. %. In embodiments, the upper bound of the amount of R₂O in the composition may be less than or equal to 28 mol. %, less than or equal to 27 mol. %, less than or equal to 26 mol. %, less than or equal to 25 mol. %, less than or equal to 24 mol. %, less than or equal to 23 mol. %, less than or equal to 22 mol. %, less than or equal to 21 mol. %, less than or equal to 20 mol. %, less than or equal to 19 mol. %, less than or equal to 18 mol. %, or even less than or equal to 17 mol. %. It should be understood that the amount of R₂O in the compositions may be within a range formed from any one of the lower bounds for R₂O and any one of the upper bounds of R₂O described herein.

For example and without limitation, the compositions may include R₂O in an amount greater than or equal to 5 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 27 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 26 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 6 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 7 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 7 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 8 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 9 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 10 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 11 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 12 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 13 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of R₂O in the composition is greater than or equal to 12 mol. % and less than or equal to 18 mol. %.

In embodiments, R₂O includes at least Li₂O. Without intending to be bound by any particular theory, it is believed that Li₂O contributes to enhanced stiffness, fracture toughness, critical strain release rate, and Young's modulus of the glass-based article. Additionally, Li⁺ has a high diffusivity through the glass matrix, which enables ion exchange times of less than 24 hours for samples thinner than 1 mm when Na⁺is ion exchanged for Li⁺ in the glass.

In embodiments of the compositions, Li₂O may be present in the composition in an amount greater than or equal to 5 mol. %. The amount of Li₂O in the composition may be less than or equal to 28 mol. %. In embodiments, Li₂O may be present in the composition in an amount greater than or equal to 9 mol. %. The amount of Li₂O in the composition may be less than or equal to 40 mol. %. If the Li₂O is too low, too few ions are available to ion exchange and the resultant stress after ion exchange is low. If, however, the Li₂O content is too high, the glass may be unstable, may exhibit a liquidus viscosity that is too low, and may have poor chemical durability. Accordingly, the amount of Li₂O in the composition may be greater than or equal to 5 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Li₂O in the composition may be greater than or equal to 9 mol. % and less than or equal to 40 mol. %. In embodiments, the lower bound of the amount of Li₂O in the composition may be greater than or equal to 5 mol. %, greater than or equal to 6 mol. %, greater than or equal to 7 mol. %, greater than or equal 8 mol. %, greater than or equal 9 mol. %, greater than or equal 10 mol. %, greater than or equal 11 mol. %, greater than or equal 12 mol. %, greater than or equal 13 mol. %, greater than or equal 14 mol. %, or greater than or equal 15 mol. %, greater than or equal 16 mol. %, or even greater than or equal to 17 mol. %. In embodiments, the upper bound of the amount of Li₂O in the composition may be less than or equal to 40 mol. %, less than or equal to 35 mol. %, less than or equal to 30 mol. %, less than or equal to 28 mol. %, less than or equal to 27 mol. %, less than or equal to 26 mol. %, less than or equal to 25 mol. %, less than or equal to 24 mol. %, less than or equal to 23 mol. %, less than or equal to 22 mol. %, less than or equal to 21 mol. %, less than or equal to 20 mol. %, less than or equal to 19 mol. %, or even less than or equal to 18 mol. %. It should be understood that the amount of Li₂O in the compositions may be within a range formed from any one of the lower bounds for Li₂O and any one of the upper bounds of Li₂O described herein.

For example and without limitation, the compositions may include Li₂O in an amount greater than or equal to 5 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 27 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 26 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 5 mol. % and less than or equal to 24 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 6 mol. % and less than or equal to 28 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 6 mol. % and less than or equal to 27 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 6 mol. % and less than or equal to 26 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 7 mol. % and less than or equal to 26 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 8 mol. % and less than or equal to 25 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 9 mol. % and less than or equal to 24 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 10 mol. % and less than or equal to 23 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 11 mol. % and less than or equal to 22 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 12 mol. % and less than or equal to 21 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 13 mol. % and less than or equal to 20 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 14 mol. % and less than or equal to 19 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 15 mol. % and less than or equal to 18 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 12 mol. % and less than or equal to 17 mol. %. In embodiments, the compositions may include Li₂O in an amount greater than or equal to 9 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 9 mol. % and less than or equal to 35 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 9 mol. % and less than or equal to 30 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 10 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 10 mol. % and less than or equal to 35 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 10 mol. % and less than or equal to 30 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 11 mol. % and less than or equal to 40 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 12 mol. % and less than or equal to 35 mol. %. In embodiments, the amount of Li₂O in the composition is greater than or equal to 13 mol. % and less than or equal to 30 mol. %.

To perform ion exchange, at least one relatively small alkali oxide ion (e.g., Li⁺ or Na⁺) is exhanged with larger alkali ions (e.g., K⁺) from an ion exchange medium. In general, the three most common types of ion exchange are Na⁺-for-Li⁺, K⁺-for-Li⁺, and K⁺-for-Na⁺. The first type, Na⁺-for-Li⁺, produces articles having a large depth of layer but a small compressive stress. The second type, K⁺-for-Li⁺, produces articles having a small depth of layer but a large compressive stress. The third type, K⁺-for-Na⁺, produces articles with intermediate depth of layer and compressive stress.

In embodiments of the compositions, the alkali oxide (R₂O) includes Na₂O. As noted herein, additions of alkali oxides such as Na₂O decrease the softening point, thereby offsetting the increase in the softening point of the composition due to SiO₂in the composition. Small amounts of Na₂O and K₂O may also help lower the liquidus temperature of the glass. However, if the amount of Na₂O is too high, the coefficient of thermal expansion of the composition becomes too high, which is undesirable. If the Na₂O or K₂O content is too high, the maximum achievable stress may be too low because the stress varies with the number of small ions in the glass that can be exchanged with larger ions external to the glass.

In embodiments, the compositions may be substantially free of Na₂O. In embodiments, the compositions may be free of Na₂O. In embodiments of the compositions that include Na₂O, the Na₂O may be present in the composition in an amount greater than 0 mol. % to improve the formability of the composition and increase the rate of ion exchange. The amount of Na₂O in the composition may be less than or equal to 7 mol. % so that the coefficient of thermal expansion is not undesirably high. Accordingly, the amount of Na₂O in embodiments of the compositions that include Na₂O is greater than 0 mol. % and less than or equal to 7 mol. %. In such embodiments, the lower bound of the amount of Na₂O in the composition may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, or even greater than or equal to 3.5 mol. %. In embodiments, the upper bound of the amount of Na₂O in the composition may be less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4 mol. %, or even less than or equal to 3.5 mol. %. It should be understood that the amount of Na₂O in the compositions may be within a range formed from any one of the lower bounds for Na₂O and any one of the upper bounds of Na₂O described herein. In embodiments, the amount of Na₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 3.5 mol. %.

For example and without limitation, the compositions that include Na₂O may include Na₂O in an amount greater than 0 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Na₂O in the composition is greater than 0 mol. % and less than or equal to 6.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the amount of Na₂O in the composition is greater than 0 mol. % and less than or equal to 5.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 6.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 6 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 5.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than 0 mol. % and less than or equal to 3.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than 0.5 mol. % and less than or equal to 3.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 1 mol. % and less than or equal to 3.5 mol. %. In embodiments, the amount of Na₂O in the composition is greater than or equal to 1.5 mol. % and less than or equal to 3.5 mol. %.

The alkali oxide in the compositions may optionally include K₂O. Like Na₂O, additions of K₂O decrease the softening point of the composition, thereby offsetting the increase in the softening point of the composition due to SiO₂in the composition. However, if the amount of K₂O is too high, the ion exchange stress will be low and the coefficient of thermal expansion of the composition becomes too high, which is undesirable. Accordingly, it is desirable to limit the amount of K₂O present in the composition.

In embodiments, the compositions may be substantially free of K₂O. In embodiments, the compositions may be free of K₂O. In embodiments where the alkali oxide includes K₂O, the K₂O may be present in the composition in an amount greater than 0 mol. %, such as greater than or equal to 0.5 or even greater than or equal to 1 mol. %, to aid in improving the formability of the composition. When present, the amount of K₂O is less than or equal to 3 mol. % or even less than or equal to 2 mol. % so that the coefficient of thermal expansion is not undesirably high. Accordingly, the amount of K₂O in embodiments of the composition that include K₂O may be greater than 0 mol. % and less than or equal to 3 mol. % or even greater than or equal to 0 mol. % and less than or equal to 2 mol. %. In such embodiments, the lower bound of the amount of K₂O in the composition may be greater than 0 mol. %, greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, or even greater than or equal to 1 mol. %. In embodiments, the upper bound of the amount of K₂O in the composition may be less than or equal to 3 mol. %, less than or equal to 2.5 mol. %, less than or equal to 2 mol. %, less than or equal to 1.75 mol. %, less than or equal to 1.5 mol. %, less than or equal to 1.25 mol. %, or even less than or equal to 1 mol. %. It should be understood that the amount of K₂O in the compositions may be within a range formed from any one of the lower bounds for K₂O and any one of the upper bounds of K₂O described herein.

For example and without limitation, the compositions having K₂O may include K₂O in an amount greater than 0 mol. % to less than or equal to 2 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1.75 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.75 mol. % and less than or equal to 1.25 mol. %. In embodiments, the amount of K₂O in the composition is about 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1.25 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 2 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1.75 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1.25 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0 mol. % and less than or equal to 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than 0 mol. % to less than or equal to 3 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 2.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 2 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.75 mol. % and less than or equal to 1.5 mol. %. In embodiments, the amount of K₂O in the composition is about 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 2 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.25 mol. % and less than or equal to 1 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 3 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 2 mol. %. In embodiments, the amount of K₂O in the composition is greater than or equal to 0.5 mol. % and less than or equal to 1.5 mol. %.

Additions of Ta₂O₅to the compositions may lower the liquidus temperature and increase the fracture toughness, Young's modulus, density, refractive index, iox exchange rate, and ion exchange stress. In embodiments, the compositions may be substantially free of Ta₂O₅. In embodiments, the compositions may be free of Ta₂O₅. In embodiments of the composition which include Ta₂O₅, the lower bound of the amount of Ta₂O₅present in the composition may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, greater than or equal to 3.5 mol. %, greater than or equal to 4 mol. %, greater than or equal to 4.5 mol. %, or even greater than or equal to 5 mol. %. In embodiments, the upper bound of the amount of Ta₂O₅in the composition may be less than or equal to 10 mol. %, less than or equal to 9.5 mol. %, less than or equal to 9 mol. %, less than or equal to 8.5 mol. %, less than or equal to 8 mol. %, less than or equal to 7.5 mol. %, less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, or even less than or equal to 5.5 mol. %. It should be understood that the amount of Ta₂O₅in the compositions may be within a range formed from any one of the lower bounds for Ta₂O₅and any one of the upper bounds of Ta₂O₅described herein.

For example and without limitation, the compositions may include Ta₂O₅in an amount greater than 0 mol. % and less than or equal to 10 mol. %. If the Ta₂O₅content is too high, the liquidus temperature may increase and the glass may become unstable and crystallize. Ta₂O₅may also increase the cost of the compositions. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 9.5 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 9 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 8.5 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 8 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 7.5 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 7 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 6.5 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 6 mol. % Ta₂O₅. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5.5 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 3 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 3.5 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than or equal to 4 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than 4.5 mol. % and less than or equal to 10 mol. % Ta₂O₅. In embodiments, the composition may include greater than 5 mol. % and less than or equal to 10 mol. % Ta₂O₅.

The compositions may further comprise one or more additional metal oxides to further improve various properties of the glass-based articles described herein. Specifically, it has been found that additions of at least one of TiO₂and ZrO₂may further increase the Young's modulus, fracture toughness and ion exchange stress. However, once the TiO₂+ZrO₂content exceeds 6 mol. % the liquidus temperature may increase and the glass may become unstable and susceptible to crystallization. It has also been found that additions of at least one of TiO₂and ZrO₂beneficially decrease the average coefficient of thermal expansion of the composition. Without wishing to be bound by theory, it is believed that the addition of at least one of TiO₂and ZrO₂improves the properties of the glass by enhancing the functionality of Al₂O₃in the composition. With respect to chemical durability, for instance, it is believed that additions of Al₂O₃to the composition reduce the amount of non-bridging oxygen in the composition which, in turn, improves the chemical durability of the glass. However, it has been found that if the amount of Al₂O₃in the composition is too high, the resistance of the composition to acid attack is diminished. It has now been found that including at least one of TiO₂and ZrO₂in addition to Al₂O₃, further reduces the amount of non-bridging oxygen in the composition which, in turn, further improves the chemical durability of the glass beyond that achievable by additions of Al₂O₃alone.

Additions of ZrO₂to the compositions may improve Young's modulus, fracture toughness, and ion exchange stress. In embodiments, the compositions may be substantially free of ZrO₂. In embodiments, the compositions may be free of ZrO₂. In embodiments of the composition which include ZrO₂, the lower bound of the amount of ZrO₂present in the composition may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, or even greater than or equal to 3 mol. %. In embodiments, the upper bound of the amount of ZrO₂in the composition may be less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4 mol. %, or even less than or equal to 3.5 mol. %. It should be understood that the amount of ZrO₂in the compositions may be within a range formed from any one of the lower bounds for ZrO₂and any one of the upper bounds of ZrO₂described herein.

For example and without limitation, the compositions may include ZrO₂in an amount greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5.5 mol. % ZrO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5 mol. % ZrO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % ZrO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4 mol. % ZrO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 6 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 6 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 6 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 6 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 6 mol. % ZrO₂. In embodiments, the composition may include greater than or equal to 3 mol. % and less than or equal to 6 mol. % ZrO₂.

In embodiments, the compositions may optionally include TiO₂. Without intending to be bound by any particular theory, it is believed that additions of TiO₂to the composition improve Young's modulus, fracture toughness, and ion exchange stress.

In embodiments, the compositions may be substantially free of TiO₂. In embodiments, the compositions may be free of TiO₂. In embodiments of the composition which include TiO₂, the lower bound of the amount of TiO₂present in the composition may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, or even greater than or equal to 3 mol. %. In embodiments, the upper bound of the amount of TiO₂in the composition may be less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4 mol. %, or even less than or equal to 3.5 mol. %. It should be understood that the amount of TiO₂in the compositions may be within a range formed from any one of the lower bounds for TiO₂and any one of the upper bounds of TiO₂described herein.

For example and without limitation, the compositions may include TiO₂in an amount greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5.5 mol. % TiO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5 mol. % TiO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % TiO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4 mol. % TiO₂. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 6 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 6 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 6 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 6 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 6 mol. % TiO₂. In embodiments, the composition may include greater than or equal to 3 mol. % and less than or equal to 6 mol. % TiO₂.

The compositions may also include one or more alkaline earth oxides or ZnO. The sum of all alkaline earth oxides and ZnO (in mol. %) is expressed herein as R′O. Specifically, R′O is the sum of MgO (mol. %), CaO (mol. %), SrO (mol. %), BaO (mol. %), and ZnO (mol. %) present in the composition. Without intending to be bound by any particular theory, it is believed that the alkaline earth oxides may be introduced in the glass to enhance various properties. For example, the addition of certain alkaline earth oxides may increase the ion exchange stress but may decrease the alkali diffusivity. R′O may also help to decrease the liquidus temperature at low concentrations. R′O may also aid in decreasing the softening point and molding temperature of the composition, thereby offsetting the increase in the softening point and molding temperature of the composition due to SiO₂in the composition. Additions of certain alkaline earth oxides may also aid in reducing the tendency of the glass to crystalize. In general, additions of alkaline earth oxide do not increase the average coefficient of thermal expansion of the composition over the temperature range from 20° C. to 300° C. as much as alternative modifiers (e.g., alkali oxides). In addition, it has been found that relatively smaller alkaline earth oxides do not increase the average coefficient of thermal expansion of the composition over the temperature range from 20° C. to 300° C. as much as larger alkaline earth oxides. For example, MgO increases the average coefficient of thermal expansion of the composition less than BaO increases the average coefficient of thermal expansion of the composition.

In embodiments, the compositions may be substantially free of alkaline earth oxides. In embodiments, the compositions may be free of alkaline earth oxides. In embodiments of the compositions including alkaline earth oxides, the alkaline earth oxides may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 8 mol. %. Without intending to be bound by any particular theory, it is believed that alkaline earth oxides and ZnO decrease alkali diffusivity and slow ion exchange. Thus, the content of alkaline earth oxides and ZnO can be minimized to prevent excessive ion exchange times for glasses with thicknesses greater than 0.5 mm. In embodiments including alkaline earth oxides, the lower bound of the amount of alkaline earth oxide in the compositions may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, greater than or equal to 3.5 mol. %, and even greater than or equal to 4 mol. %. In such embodiments, the upper bound of the amount of alkaline earth oxide in the composition may be less than or equal to 8 mol. %, less than or equal to 7.5 mol. %, less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4 mol. %, or even less than or equal to 3.5 mol. %. It should be understood that the amount of alkaline earth oxide in the compositions may be within a range formed from any one of the lower bounds for alkaline earth oxide and any one of the upper bounds of alkaline earth oxide described herein.

For example and without limitation, the compositions may include alkaline earth oxide in an amount greater than 0 mol. % and less than or equal to 8 mol. %. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 7.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 7 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 6.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 6 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1.0 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 3 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 3.5 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 4 mol. % and less than or equal to 8 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 1.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 3.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 3 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2.5 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2 mol. % alkaline earth oxide. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 1.5 mol. % alkaline earth oxide.

In embodiments of the compositions described herein, the alkaline earth oxide in the composition may optionally include MgO. Without intending to be bound by any particular theory, it is believed that in addition to improving the formability and the meltability of the composition, MgO may also increase the viscosity of the glass and reduce the tendency of the glass to crystalize. Too much MgO tends to cause crystallization in the glass, decreasing the liquidus viscosity and decreasing formability.

In embodiments, the compositions may be substantially free of MgO. In embodiments, the compositions may be free of MgO. In embodiments where the composition includes MgO, the MgO may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 5 mol. %. In embodiments including MgO, the lower bound of the amount of MgO in the compositions may be greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, greater or equal to 2.0 mol. %, greater or equal to 2.25 mol. %, or even greater than or equal to 2.5 mol. %. In such embodiments, the upper bound of the amount of MgO in the composition may be less than or equal to 5 mol. %, less than or equal to 4.75 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4.25 mol. %, less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, or even less than or equal to 2.75 mol. %. It should be understood that the amount of MgO in the compositions may be within a range formed from any one of the lower bounds for MgO and any one of the upper bounds of MgO described herein.

For example and without limitation, the compositions may include MgO in an amount greater than 0 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.75 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.25 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.75 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.25 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3 mol. % MgO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.75 mol. % MgO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 1.25 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 1.75 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 2.25 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 5 mol. % MgO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % MgO.

In embodiments of the compositions described herein, the alkaline earth oxide in the composition may optionally include CaO. Without intending to be bound by any particular theory, it is believed that in addition to improving the formability and the meltability of the composition, CaO may also lower the liquidus temperature in small amounts while improving chemical durability and lowering the CTE. If the CaO content is too high (or if the MgO+CaO content is too high) then the liquidus temperature can increase and degrade the liquidus viscosity.

In embodiments, the compositions may be substantially free of CaO. In embodiments, the compositions may be free of CaO. In embodiments where the composition includes CaO, the CaO may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 5 mol. %. In embodiments including CaO, the lower bound of the amount of CaO in the compositions may be greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, greater or equal to 2.0 mol. %, greater or equal to 2.25 mol. %, or even greater than or equal to 2.5 mol. %. In such embodiments, the upper bound of the amount of CaO in the composition may be less than or equal to 5 mol. %, less than or equal to 4.75 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4.25 mol. %, less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, or even less than or equal to 2.75 mol. %. It should be understood that the amount of CaO in the compositions may be within a range formed from any one of the lower bounds for CaO and any one of the upper bounds of CaO described herein.

For example and without limitation, the compositions may include CaO in an amount greater than 0 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.75 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.25 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.75 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.25 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3 mol. % CaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.75 mol. % CaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 1.25 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 1.75 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 2.25 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 5 mol. % CaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % CaO.

In the embodiments described herein, the alkaline earth oxide in the compositions may optionally include SrO. Without intending to be bound by any particular theory, it is believed that in addition to improving the formability and the meltability of the composition, SrO may also reduce the tendency of the glass to crystalize. Too much SrO changes the liquidus viscosity and may increase the CTE of the glass.

In embodiments, the compositions may be substantially free of SrO. In embodiments, the compositions may be free of SrO. In embodiments where the composition includes SrO, the SrO may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 5 mol. %. In embodiments including SrO, the lower bound of the amount of SrO in the compositions may be greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, greater or equal to 2.0 mol. %, greater or equal to 2.25 mol. %, or even greater than or equal to 2.5 mol. %. In such embodiments, the upper bound of the amount of SrO in the composition may be less than or equal to 5 mol. %, less than or equal to 4.75 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4.25 mol. %, less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, or even less than or equal to 2.75 mol. %. It should be understood that the amount of SrO in the compositions may be within a range formed from any one of the lower bounds for SrO and any one of the upper bounds of SrO described herein.

For example and without limitation, the compositions may include SrO in an amount greater than 0 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.75 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.5 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4.25 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 4 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.75 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.5 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3.25 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 3 mol. % SrO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.75 mol. % SrO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 1.25 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 1.75 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 2.25 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 5 mol. % SrO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % SrO.

In embodiments, the compositions may be substantially free of BaO. In embodiments, the compositions may be free of BaO. In embodiments where the composition includes BaO, the BaO may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 3 mol. %. In embodiments including BaO, the lower bound of the amount of BaO in the compositions may be greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, or even greater or equal to 1 mol. %. In such embodiments, the upper bound of the amount of BaO in the composition may be less than or equal to 3 mol. %, less than or equal to 2.75 mol. %, less than or equal to 2.5 mol. %, less than or equal to 2.25 mol. %, less than or equal to 2 mol. %, less than or equal to 1.75 mol. %, or even less than or equal to 1.5 mol. It should be understood that the amount of BaO in the compositions may be within a range formed from any one of the lower bounds for BaO and any one of the upper bounds of BaO described herein.

For example and without limitation, the compositions may include BaO in an amount greater than 0 mol. % and less than or equal to 3 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.75 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.5 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2.25 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 2 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 1.75 mol. % BaO. In embodiments, the composition may include greater than 0 mol. % and less than or equal to 1.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 3 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 2.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 2.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 2.25 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 2 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 1.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.25 mol. % and less than or equal to 1.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.25 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 1.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 1.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 3 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 2.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 2.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 2.25 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 2 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 1.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 1.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 3 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2.5 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2.25 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 2 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 1.75 mol. % BaO. In embodiments, the composition may include greater than or equal to 1 mol. % and less than or equal to 1.5 mol. % BaO.

The compositions may further include ZnO as a modifier of the composition. Without intending to be bound by any particular theory, it is believed that additions of ZnO to the composition decrease the softening point and molding temperature of the composition, thereby offsetting the increase in the softening point and molding temperature of the composition due to SiO₂in the composition. ZnO may also increase the stress after ion exchange, but decrease the diffusivity of alkali ions and slow ion exchange. Significantly, additions of ZnO do not increase the average coefficient of thermal expansion of the composition over the temperature range from 20° C. to 300° C. as much as some other modifiers (e.g., alkali oxides and/or the alkaline earth oxides CaO and SrO). As such, the benefit of using additions of ZnO to reduce the softening point and molding temperature can be maximized without a significant increase in the average coefficient of thermal expansion of the composition. In this regard, ZnO has a similar effect on the composition as MgO (e.g., it reduces the softening point and molding temperature of the composition without significantly increasing the average coefficient of thermal expansion). However, additions of ZnO to achieve these characteristics are favored over additions of MgO because ZnO has a more pronounced effect on the softening point and ZnO does not promote nucleation and crystallization in the glass as much as MgO.

In embodiments, the compositions may be substantially free of ZnO. In embodiments, the compositions may be free of ZnO. If the concentration of ZnO is too high the liquidus temperature may increase and the rate of ion exchange may decrease. In embodiments where the composition includes ZnO, the ZnO may be present in an amount greater than 0 mol. %, such as greater than or equal to 0.5 mol. %, and less than or equal to 4 mol. %. In embodiments including ZnO, the lower bound of the amount of ZnO in the compositions may be greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, greater or equal to 2.0 mol. %, greater or equal to 2.25 mol. %, or even greater than or equal to 2.5 mol. %. In such embodiments, the upper bound of the amount of ZnO in the composition may be less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, or even less than or equal to 2.75 mol. %. It should be understood that the amount of ZnO in the compositions may be within a range formed from any one of the lower bounds for ZnO and any one of the upper bounds of ZnO described herein.

For example and without limitation, the compositions may include ZnO in an amount greater than or equal to 0.5 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3.75 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3.5 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3.25 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 3 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.75 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.75 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 1.0 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 1.25 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 1.5 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 1.75 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 2 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 2.25 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 2.5 mol. % and less than or equal to 4 mol. % ZnO. In embodiments, the composition may include greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. % ZnO.

The compositions may further include rare earth metal oxides (RE₂O₃). The rare earth metal may be selected from Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, and combinations thereof. RE₂O₃may increase the Young's modulus and stress after ion exchange, as well as increase the fracture toughness and density. However, RE₂O₃may decrease alkali ion diffusivity and increase the liquidus temperature at high concentrations.

In embodiments, the compositions may be substantially free of RE₂O₃. In embodiments, the compositions may be free of RE₂O₃. In embodiments of the compositions that include RE₂O₃, the RE₂O₃may be present in the composition in an amount greater than 0 mol. %. In such embodiments, the RE₂O₃may be present in the composition in an amount less than or equal to 8 mol. %. Accordingly, in the embodiments in which RE₂O₃is present, the compositions generally comprise RE₂O₃in an amount greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, greater than or equal to 3.5 mol. %, or even greater than or equal to 4 mol. %. In embodiments, the upper bound of the amount of RE₂O₃may be less than or equal to 8 mol. %, less than or equal to 7.5 mol. %, less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, or even less than or equal to 4.5 mol. %. It should be understood that the amount of RE₂O₃in the compositions may be within a range formed from any one of the lower bounds for RE₂O₃and any one of the upper bounds of RE₂O₃described herein.

For example and without limitation, the compositions having RE₂O₃may include RE₂O₃in an amount greater than 0 mol. % to less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 7.5 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 6.5 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 5.5 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.5 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 1 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 1.5 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 2 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 2.5 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 3 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 3.5 mol. % and less than or equal to 8 mol. %. In embodiments, the amount of RE₂O₃in the composition is greater than or equal to 4 mol. % and less than or equal to 8 mol. %.

An exemplary RE₂O₃is Y₂O₃. In embodiments, the compositions may be substantially free of Y₂O₃. In embodiments, the compositions may be free of Y₂O₃. In embodiments of the compositions that include Y₂O₃, the Y₂O₃may be present in the composition in an amount greater than 0 mol. %. Y₂O₃is the lightest of the RE₂O₃oxides (except Sc₂O₃, which may be prohibitively expensive) and thus may increase the specific modulus more than any other of the RE₂O₃oxides. Y₂O₃may increase ion exchange stress and fracture toughness. It also does not typically impart any color to the glass, unlike the oxides of Ce, Pr, Nd, Pm, Sm, Eu, Tb, Dy, Ho, Er, and Tm. Y₂O₃may also decrease the diffusivity of alkali ions and thus slow ion exchange rates. It may also raise the liquidus temperature at high concentrations and increases batch cost. In such embodiments, the Y₂O₃may be present in the composition in an amount less than or equal to 7 mol. %. Accordingly, in the embodiments in which Y₂O₃is present, the compositions generally comprise Y₂O₃in an amount greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, or even greater than or equal to 3.5 mol. %. In embodiments, the upper bound of the amount of Y₂O₃may be less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, less than or equal to 4.5 mol. %, or even less than or equal to 4 mol. %. It should be understood that the amount of Y₂O₃in the compositions may be within a range formed from any one of the lower bounds for Y₂O₃and any one of the upper bounds of Y₂O₃described herein.

For example and without limitation, the compositions having Y₂O₃may include Y₂O₃in an amount greater than 0 mol. % to less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 6.5 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 5.5 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.5 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than 0 mol. % and less than or equal to 4 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 1 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 1.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 2 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 2.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 3 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 3.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of Y₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 7 mol. %.

An exemplary RE₂O₃is La₂O₃. In embodiments, the compositions may be substantially free of La₂O₃. In embodiments, the compositions may be free of La₂O₃. In embodiments of the compositions that include La₂O₃, the La₂O₃may be present in the composition in an amount greater than 0 mol. %. In such embodiments, the La₂O₃may be present in the composition in an amount less than or equal to 5 mol. %. La₂O₃may increase ion exchange stress and fracture toughness, and it may help to suppress crystallization in small concentrations. It also does not typically impart any color to the glass, unlike the oxides of Ce, Pr, Nd, Pm, Sm, Eu, Tb, Dy, Ho, Er, and Tm. La₂O₃may also decrease the diffusivity of alkali ions and thus slow ion exchange rates. It may also raise the liquidus temperature at high concentrations and increase batch cost. Accordingly, in the embodiments in which La₂O₃is present, the compositions generally comprise La₂O₃in an amount greater than 0 mol. %, greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.25 mol. %, or even greater than or equal to 2.5 mol. %. In embodiments, the upper bound of the amount of La₂O₃may be less than or equal to 5 mol. %, less than or equal to 4.75 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4.25 mol. %, less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, or even less than or equal to 2.75 mol. %. It should be understood that the amount of La₂O₃in the compositions may be within a range formed from any one of the lower bounds for La₂O₃and any one of the upper bounds of La₂O₃described herein.

For example and without limitation, the compositions having La₂O₃may include La₂O₃in an amount greater than 0 mol. % to less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.75 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.25 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 4 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 3.75 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 3.5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 3.25 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 3 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than 0 mol. % and less than or equal to 2.75 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 0.25 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 0.75 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 1 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 1.25 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 1.5 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 1.75 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 2 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 2.25 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 2.5 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of La₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 2.5 mol. %.

Boron oxide (B₂O₃) is a glass former which may be added to the compositions to reduce the viscosity of the glass at a given temperature thereby improving the formability of the glass. Said differently, additions of B₂O₃to the glass decrease the strain, anneal, softening, and molding temperatures of the composition, thereby improving the formability of the glass. As such, additions of B₂O₃may be used to offset the decrease in formability of compositions having relatively higher amounts of SiO₂. B₂O₃also helps to lower the liquidus temperature and suppress crystallization. However, it has been found that if the amount of B₂O₃in the composition is too high, the diffusivity of alkali ions in the glass is low, the rate of ion exchange is decreased, and the stress achieved after ion exchange is decreased.

In embodiments, the compositions may be free of B₂O₃. In other embodiments, the compositions may be substantially free of B₂O₃. In other embodiments, the compositions may include B₂O₃in a concentration greater than 0 mol. % to enhance the formability of the compositions, when present. The concentration of B₂O₃may be less than or equal to 7 mol. % such that reasonable ion exchange times and satisfactory stress can be achieved after ion exchange. Accordingly, in the embodiments in which B₂O₃is present, the compositions generally comprise B₂O₃in an amount greater than 0 mol. % and less than or equal to 7 mol. %. In such embodiments, the lower bound of the amount of B₂O₃in the composition may be greater than 0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 2 mol. %, greater than or equal to 2.5 mol. %, greater than or equal to 3 mol. %, greater than or equal to 3.5 mol. %, or even greater than or equal to 4 mol. %. In embodiments, the upper bound of the amount of B₂O₃in the compositions may be less than or equal to 7 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6 mol. %, less than or equal to 5.5 mol. %, less than or equal to 5 mol. %, or even less than or equal to 4.5 mol. %. It should be understood that the amount of B₂O₃in the compositions may be within a range formed from any one of the lower bounds for B₂O₃and any one of the upper bounds of B₂O₃described herein.

For example and without limitation, the compositions may include B₂O₃in an amount greater than 0 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 0.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 1 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 1.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 2 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 2.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 3 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 3.5 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 4 mol. % and less than or equal to 7 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than 0 mol. % and less than or equal to 6.5 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than 0 mol. % and less than or equal to 6 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than 0 mol. % and less than or equal to 5.5 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than 0 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than 0 mol. % and less than or equal to 4.5 mol. %. In embodiments, the amount of B₂O₃in the composition is greater than or equal to 1.5 mol. % and less than or equal to 5 mol. %.

The compositions may also include P₂O₅. Without intending to be bound by any particular theory, it is believed that P₂O₅improves damage resistance and increases the rate of ion exchange. P₂O₅may also lower the liquidus temperature, which improves the liquidus viscosity. In some embodiments, the addition of phosphorous to the glass creates a structure in which SiO₂is replaced by tetrahedrally coordinated aluminum and phosphorus (AlPO₄) as a glass former.

In embodiments, the compositions may be free of P₂O₅. In other embodiments, the compositions may be substantially free of P₂O₅. In other embodiments, the compositions may include P₂O₅in a concentration of greater than 0 mol. %. The compositions may include P₂O₅in a concentration less than or equal to 5 mol. %, because if the P₂O₅content is too high, the fracture toughness and stress achieved with ion exchange may be decreased. Accordingly, in the embodiments in which P₂O₅is present, the compositions generally comprise P₂O₅in an amount greater than 0 mol. % and less than or equal to 5 mol. %. In such embodiments, the lower bound of the amount of P₂O₅in the composition may be greater than 0 mol. %, greater than or equal to 0.25 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 0.75 mol. %, greater than or equal to 1 mol. %, greater than or equal to 1.25 mol. %, greater than or equal to 1.5 mol. %, greater than or equal to 1.75 mol. %, or even greater than or equal to 2 mol. %. In embodiments, the upper bound of the amount of P₂O₅in the compositions may be less than or equal to 4.75 mol. %, less than or equal to 4.5 mol. %, less than or equal to 4.25 mol. %, less than or equal to 4 mol. %, less than or equal to 3.75 mol. %, less than or equal to 3.5 mol. %, less than or equal to 3.25 mol. %, less than or equal to 3 mol. %, less than or equal to 2.75 mol. %, less than or equal to 2.5 mol. %, or even less than or equal to 2.25 mol. %. It should be understood that the amount of P₂O₅in the compositions may be within a range formed from any one of the lower bounds for P₂O₅and any one of the upper bounds of P₂O₅described herein.

For example and without limitation, the compositions including P₂O₅may include P₂O₅in an amount greater than 0 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 0.25 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 0.5 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 0.75 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 1 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 1.25 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 1.5 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 1.75 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than or equal to 2 mol. % and less than or equal to 5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 4.75 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 4.5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 4.25 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 4 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 3.75 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 3.5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 3.25 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 3 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 2.75 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 2.5 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 0 mol. % and less than or equal to 2.25 mol. %. In embodiments, the amount of P₂O₅in the composition is greater than 1 mol. % and less than or equal to 3.5 mol. %.

In the embodiments, the compositions may be substantially free or free of other constituent components including, without limitation, Fe₂O₃, SnO₂, As₂O₃, Sb₂O₃, and PbO. In embodiments, the compositions may include small quantities of other constituent components including, without limitation, Fe₂O₃and SnO₂. For example, the compositions including SnO₂may include greater than 0 mol. % to 0.2 mol. % SnO₂. In the same or different embodiments, the compositions including Fe₂O₃may include greater than 0 mol. % to 0.1 mol. % Fe₂O₃. Fe₂O₃and SnO₂can act as fining agents and help remove bubbles during melting and fining of the composition. Thus it may be beneficial to have one or more multivalent fining agents such as Fe₂O₃, SnO₂, CeO₂, or MnO₂in the glass. In embodiments, SnO₂may be used as a fining agent, and it may not impart any color to the glass. In embodiments, the composition may include greater than or equal to 0.05 mol. % and less than or equal to 0.15 mol. % SnO₂.

In embodiments, the composition may include various compositional relationships. For example, the concentrations of R₂O, R′O, Al₂O₃, Ta₂O₅, RE₂O₃, ZrO₂, and TiO₂may be related as shown in relationship (III):

−8 mol. %≤R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂≤8 mol. % (III)

Without intending to be bound by any particular theory, it is believed that while R₂O, R′O and RE₂O₃can create non-bridging oxygens in the glass network, Al₂O₃, Ta₂O₅, ZrO₂, and to a certain extent TiO₂, can act as intermediates and convert these non bridging oxygens back into bridging oxygens and increase the ion exchange rate and stress levels in the glass, as well as increase the elastic modulus and fracture toughness. If the quantity gets too high, however, then the glass may suffer from low ion exchange stress and fracture toughness. If the quantity gets too low, then the liquidus temperature of the glass can get too high and the glass stability may suffer. Therefore it is desirable to keep the quantity of relationship (VI) to within about 8 mol. % of O. For instance, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −7 mol. % to less than or equal to 7 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −6 mol. % to less than or equal to 6 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −5 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −4 mol. % to less than or equal to 4 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −3 mol. % to less than or equal to 3 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −2 mol. % to less than or equal to 2 mol. %. In embodiments, R₂O+R′P−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −1 mol. % to less than or equal to 1 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −8 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −7 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may range from greater than or equal to −6 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may be about 0 mol. %. It should be understood that R₂O+−Al₂O₃−Ta₂O₅+1.5*RE₂O₃−ZrO₂−TiO₂may be within a range formed from any one of the lower bounds for the relationship and any one of the upper bounds for the relationship described herein.

In embodiments, the concentrations of R₂O, A1₂O₃, and Ta₂O₅may be related as shown in relationship (IV):

−12 mol. %≤R₂O−Al₂O₃−Ta₂O₅≤6 mol. % (IV)

For instance, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −11 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −10 mol. % to less than or equal to 4 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −9 mol. % to less than or equal to 3 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −8 mol. % to less than or equal to 2 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −7 mol. % to less than or equal to 1 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −6 mol. % to less than or equal to 0 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −5 mol. % to less than or equal to −1 mol. %. In embodiments, R₂O−Al₂O₃−Ta₂O₅may range from greater than or equal to −4 mol. % to less than or equal to −2 mol. %. In embodiments, R₂O−A1₂O₃−Ta₂O₅may be about −3 mol. %. It should be understood that R₂O−Al₂O₃−Ta₂O₅may be within a range formed from any one of the lower bounds for the relationship and any one of the upper bounds for the relationship described herein. Without intending to be bound by any particular theory, it is believed that Al₂O₃and Ta₂O₅can coordinate with the alkali oxides to provide a glass structure that has both high fracture toughness and high alkali diffusivity for fast ion exchange and high stress after ion exchange.

In embodiments, the concentrations of R₂O, R′O, Al₂O₃, and Ta₂O₅may be related as shown in relationship (V):

−7 mol. %≤R₂O+R′O−Al₂O₃−Ta₂O₅≤9 mol. % (V)

For instance, R₂O+R′O−Al₂O₃−Ta₂O₅may range from greater than or equal to −6 mol. % to less than or equal to 8 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅may range from greater than or equal to −5 mol. % to less than or equal to 7 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅may range from greater than or equal to −4 mol. % to less than or equal to 6 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅may range from greater than or equal to −3 mol. % to less than or equal to 5 mol. %. In embodiments, R₂O+−Al₂O₃−Ta₂O₅may range from greater than or equal to −2 mol. % to less than or equal to 4 mol. %. In embodiments, R₂O+−Al₂O₃−Ta₂O₅may range from greater than or equal to −1 mol. % to less than or equal to 3 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅may range from greater than or equal to 0 mol. % to less than or equal to 2 mol. %. In embodiments, R₂O+R′O−Al₂O₃−Ta₂O₅may be about 1 mol. %. It should be understood that R₂O+R′O−Al₂O₃−Ta₂O₅may be within a range formed from any one of the lower bounds for the relationship and any one of the upper bounds for the relationship described herein. Without intending to be bound by any particular theory, it is believed that balancing the excess modifiers by keeping the quantity R₂O+R′O−Al₂O₃−Ta₂O₅close to about 0 may improve ion exchange rate, ion exchange stress, and also may increase modulus and critical energy release rate.

In embodiments, the total amount of ZrO₂, TiO₂, and SnO₂(i.e., ZrO₂(mol. %)+TiO₂(mol. %)+SnO₂(mo.%)) may be in the range from greater than or equal to 0 mol. % to less than or equal to 2 mol. %, from greater than or equal to 0 mol % to less than or equal to 1.75 mol. %, from greater than or equal to 0 mol. % to less than or equal to 1.5 mol. %, greater than or equal to 0 mol. % to less than or equal to 1.25 mol. %, from greater than or equal to 0.25 mol. % to less than or equal to 2 mol. %, from greater than or equal to 0.25 mol % to less than or equal to 1.75 mol. %, from greater than or equal to 0.25 mol. % to less than or equal to 1.5 mol. %, greater than or equal to 0.25 mol. % to less than or equal to 1.25 mol. %, from greater than or equal to 0.5 mol. % to less than or equal to 2 mol. %, from greater than or equal to 0.5 mol % to less than or equal to 1.75 mol. %, from greater than or equal to 0.5 mol. % to less than or equal to 1.5 mol. %, greater than or equal to 0.5 mol. % to less than or equal to 1.25 mol. %, from greater than or equal to 0.75 mol. % to less than or equal to 2 mol. %, from greater than or equal to 0.75 mol % to less than or equal to 1.75 mol. %, from greater than or equal to 0.75 mol. % to less than or equal to 1.5 mol. %, greater than or equal to 0.75 mol. % to less than or equal to 1.25 mol. %, from greater than or equal to 1 mol. % to less than or equal to 2 mol. %, from greater than or equal to 1 mol % to less than or equal to 1.75 mol. %, from greater than or equal to 1 mol. % to less than or equal to 1.5 mol. %, or even greater than or equal to 1 mol. % to less than or equal to 1.25 mol. %. It should be understood that the the total amount of ZrO₂, TiO₂, and SnO₂(i.e., ZrO₂(mol. %)+TiO₂(mol. %)+SnO₂(mo.%)) may be within a range formed from any one of the lower bounds for the amount and any one of the upper bounds for the amount described herein.

In embodiments, the ratio of the amount of Li₂O (in mol. %) to the total amount of R₂O (in mol. %) may be in the range from greater than or equal to 0.5 to less than or equal to 1, from greater than or equal to 0.55 to less than or equal to 1, from greater than or equal to 0.6 to less than or equal to 1, from greater than or equal to 0.65 to less than or equal to 1, from greater than or equal to 0.7 to less than or equal to 1, from greater than or equal to 0.75 to less than or equal to 1, from greater than or equal to 0.8 to less than or equal to 1, from greater than or equal to 0.85 to less than or equal to 1, from greater than or equal to 0.9 to less than or equal to 1, or even from greater than or equal to 0.95 to less than or equal to 1. It should be understood that the relationship of the ratio of the amount of Li₂O (in mol. %) to the total amount of R₂O (in mol. %) may be within a range formed from any one of the lower bounds for the relationship and any one of the upper bounds for the relationship described herein. Without intending to be bound by any particular theory, it is believed that a high ratio of Li₂O to total R₂O may increase the elastic modulus and achievable ion exchange stress.

In embodiments, the concentrations of Li₂O, Al₂O₃, and Ta₂O₅may be related as shown in relationship (VI):

$\begin{matrix} 0.4 \leq \frac{{Li}_{2} O}{({Al}_{2} O_{3} + {Ta}_{2} O_{5})} \leq 1.5 & (VI) \end{matrix}$

For instance, the ratio of relationship (IX) may range from greater than or equal to 0.45 to less than or equal to 1.45, from greater than or equal to 0.5 to less than or equal to 1.4, from greater than or equal to 0.55 to less than or equal to 1.35, from greater than or equal to 0.6 to less than or equal to 1.3, from greater than or equal to 0.65 to less than or equal to 1.25, from greater than or equal to 0.7 to less than or equal to 1.2, from greater than or equal to 0.75 to less than or equal to 1.15, from greater than or equal to 0.8 to less than or equal to 1.1, from greater than or equal to 0.85 to less than or equal to 1.05, from greater than or equal to 0.9 to less than or equal to 1, or even equal to about 0.95. It should be understood that the ratio of relationship (IX) may be within a range formed from any one of the lower bounds for the relationship and any one of the upper bounds for the relationship described herein. Without intending to be bound by any particular theory, it is believed that Li₂O may be the primary ion for chemical strengthening in the described glasses. The highest stress and highest Na⁺for Li⁺ diffusivity occurs when there is minimal Na₂O in the glass and when the Li₂O content is nearly fully compensated by Al₂O₃or Ta₂O₅, where the ratio of Li₂O to (Al₂O₃+Ta₂O₅) will be close to 1. Thus it may be advantageous to have the ratio of Li₂O to (Al₂O₃+Ta₂O₅) greater than 0.4 and less than 1.5 or even greater than 0.75 and less than 1.25. When the ratio is less than 0.4 or greater than 1.5, it is believed that the ion exchange stress and rate will both suffer.

The compositions may be formed by mixing a batch of glass raw materials (e.g., powders of SiO₂, Al₂O₃, alkali carbonates, nitrates, or sulfates, alkaline earth carbonates, nitrates, sulfates, or oxides, and the like) such that the batch of glass raw materials has the desired composition. Common minerals such as spodumene and nepheline syenite may also be convenient sources of alkalis, alumina, and silica. Fining agents such as CeO₂, Fe₂O₃, and/or SnO₂may also be added to aid in fining (bubble removal). Nitrates may also be added to fully oxidize the fining agents for optimal efficacy. Thereafter, the batch of glass raw materials may be heated to form a molten composition which is subsequently cooled and solidified to form a glass comprising the composition. During cooling (i.e., when the composition is plastically deformable) the glass comprising the composition may be shaped using standard forming techniques to shape the composition into a desired final form, providing a glass-based article comprising the composition. Alternatively, the glass article may be shaped into a stock form, such as a sheet, tube, or the like, and subsequently reheated and formed into the desired final form, such as by molding or the like.

From the above compositions, glass substrates according to embodiments may be formed by any suitable method, for example slot forming, float forming, rolling processes, down-draw processes, fusion forming processes, or updraw processes. The glass composition and the substrates produced therefrom may be characterized by the manner in which it may be formed. For instance, the glass composition may be characterized as float-formable (i.e., capable of being formed by a float process), down-drawable and, in particular, fusion-formable or slot-drawable (i.e., formed by a down draw process such as a fusion draw process or a slot draw process).

Some embodiments of the glass substrates described herein may be formed by a down-draw process. Down-draw processes produce glass substrates having a uniform thickness that possess relatively pristine surfaces. Because the average flexural strength of the glass substrate is controlled by the amount and size of surface flaws, a pristine surface that has had minimal contact has a higher initial strength. In addition, down drawn glass substrates have a very flat, smooth surface that can be used in its final application without costly grinding and polishing.

Some embodiments of the glass substrates described herein may be fusion-formable (i.e., formable using a fusion draw process). The fusion process uses a drawing tank that has a channel for accepting molten glass raw material. The channel has weirs that are open at the top along the length of the channel on both sides of the channel. When the channel fills with molten material, the molten glass overflows the weirs. Due to gravity, the molten glass flows down the outside surfaces of the drawing tank as two flowing glass films. These outside surfaces of the drawing tank extend down and inwardly so that they join at an edge below the drawing tank. The two flowing glass films join at this edge to fuse and form a single flowing glass substrate. The fusion draw method offers the advantage that, because the two glass films flowing over the channel fuse together, neither of the outside surfaces of the resulting glass substrate comes in contact with any part of the apparatus. Thus, the surface properties of the fusion drawn glass substrate are not affected by such contact.

Some embodiments of the glass substrates described herein may be formed by a slot draw process. The slot draw process is distinct from the fusion draw method. In slot draw processes, the molten raw material glass is provided to a drawing tank. The bottom of the drawing tank has an open slot with a nozzle that extends the length of the slot. The molten glass flows through the slot/nozzle and is drawn downward as a continuous glass substrate and into an annealing region.

Drawing processes for forming glass substrates, such as, for example, glass sheets, are desirable because they allow a thin glass substrate to be formed with few defects. It was previously thought that glass compositions were required to have relatively high liquidus viscosities—such as a liquidus viscosity greater than 1000 kP, greater than 1100 kP, or greater than 1200 kP—to be formed by a drawing process, such as, for example, fusion drawing or slot drawing. However, developments in drawing processes may allow glasses with lower liquidus viscosities to be used in drawing processes.

The glass-based articles described herein have relatively high fracture toughness and critical strain energy release rates, and can be ion exchanged to achieve parabolic stress profiles with relatively high central tension, such that the glass-based articles made from the compositions have enhanced drop performance relative to previously known articles.

In embodiments, the glass-based article described herein may have a fracture toughness K_1Cof greater than or equal to 0.72 MPa√m. For example, the fracture toughness may be greater than or equal to 0.75 MPa√m, greater than or equal to 0.8 MPa√m, or even greater than or equal to 0.85 MPa√m. A high fracture toughness may beneficial to prevent the propagation of cracks and also increase the stored strain energy limit. High A1₂O₃, Ta₂O₅, and RE₂O₃contents all contribute to increased fracture toughness while P₂O₅lowers it, as described above.

In embodiments, the glass-based article described herein may have a critical strain energy release rate G_1Cof greater than 7 J/m². For example, the critical strain energy release rate may be greater than or equal to 7.5 J/m², greater than or equal to 8 J/m², or even greater than or equal to 8.5 J/m². The critical strain energy release rate is the energy it takes to create new crack surfaces, so the higher that energy the more impact energy the glass can withstand before generating cracks. A higher critical strain energy release rate also means that more impact energy is dissipated per unit length of crack generated. Thus the higher the critical strain energy release rate, the better the drop performance for the same stress profile.

In embodiments, the glass-based article described herein may have a Young's modulus E of greater than 70 GPa. For example, the Young's modulus may be greater than or equal to 75 GPa, greater than or equal to 80 GPa, or even greater than or equal to 85 GPa. The higher the elastic modulus, the greater the stress generated by ion exchange and the stronger the compressive layer.

When strengthened by ion exchange, the glass-based articles described herein may have a compressive stress region extending from a first surface to a depth of compression. The glass based article may have a tensile stress region extending from the depth of compression on one side to the depth of compression on the other side. The tensile stress region may have a maximum CT greater than or equal to 175 MPa. In embodiments, this maximum CT may range from greater than or equal to 175 MPa to less than or equal to 600 MPa, from greater than or equal to 200 MPa to less than or equal to 575 MPa, from greater than or equal to 225 MPa to less than or equal to 550 MPa, from greater than or equal to 250 MPa to less than or equal to 525 MPa, from greater than or equal to 275 MPa to less than or equal to 500 MPa, from greater than or equal to 300 MPa to less than or equal to 475 MPa, from greater than or equal to 325 MPa to less than or equal to 450 MPa, from greater than or equal to 350 MPa to less than or equal to 425 MPa, from greater than or equal to 250 MPa to less than or equal to 325 MPa, or even from greater than or equal to 375 MPa to less than or equal to 400 MPa. It should be understood that the maximum CT may be within a range formed from any one of the lower bounds for the maximum CT and any one of the upper bounds for the maximum CT described herein.

When strengthened by ion exchange, the glass-based articles described herein may have a stored strain energy of greater than 20 J/m². For example, the stored strain energy may be greater than or equal to 30 J/m², greater than or equal to 40 J/m², greater than or equal to 50 J/m², greater than or equal to 60 J/m², greater than or equal to 70 J/m², greater than or equal to 80 J/m², greater than or equal to 90 J/m², greater than or equal to 100 J/m², greater than or equal to 200 J/m², greater than or equal to 300 J/m², greater than or equal to 400 J/m², or even greater than or equal to 500 J/m².

When strengthened by ion exchange, the tensile stress region may have a maximum CT greater than or equal to 175 MPa and the glass-based article may comprise a critical strain energy release rate G_1Cgreater than or equal to 7 J/m². For example, the maximum CT may range from greater than or equal to 175 MPa to less than or equal to 600 MPa, from greater than or equal to 200 MPa to less than or equal to 575 MPa, from greater than or equal to 225 MPa to less than or equal to 550 MPa, from greater than or equal to 250 MPa to less than or equal to 525 MPa, from greater than or equal to 275 MPa to less than or equal to 500 MPa, from greater than or equal to 300 MPa to less than or equal to 475 MPa, from greater than or equal to 325 MPa to less than or equal to 450 MPa, from greater than or equal to 350 MPa to less than or equal to 425 MPa, or even from greater than or equal to 375 MPa to less than or equal to 400 MPa. Also, the critical strain energy release rate may be greater than or equal to 7.5 J/m²or even greater than or equal to 8 J/m².

In the same or different embodiments, an arithmetic product of the critical strain energy release rate and the maximum CT (G_1C×CT) may be greater than or equal to 1450 MPa·J/m², greater than or equal to 2000 MPa·J/m², greater than or equal to 2500 MPa·J/m², greater than or equal to 3000 MPa·J/m², greater than or equal to 3500 MPa·J/m², greater than or equal to 4000 MPa·J/m², or even greater than or equal to 4100 MPa·J/m².

When strengthened by ion exchange, the tensile stress region may have a maximum CT greater than or equal to 175 MPa and the glass-based article may comprise a fracture toughness K_1Cgreater than or equal to 0.7 MPa√m. For example, the maximum CT may range from greater than or equal to 175 MPa to less than or equal to 600 MPa, from greater than or equal to 200 MPa to less than or equal to 575 MPa, from greater than or equal to 225 MPa to less than or equal to 550 MPa, from greater than or equal to 250 MPa to less than or equal to 525 MPa, from greater than or equal to 275 MPa to less than or equal to 500 MPa, from greater than or equal to 300 MPa to less than or equal to 475 MPa, from greater than or equal to 325 MPa to less than or equal to 450 MPa, from greater than or equal to 350 MPa to less than or equal to 425 MPa, or even from greater than or equal to 375 MPa to less than or equal to 400 MPa. Also, the fracture toughness may be greater than or equal to 0.75 MPa√m or even greater than or equal to 0.8 MPa√m.

In the same or different embodiments, an arithmetic product of the fracture toughness and the maximum CT (K_1C×CT) may be greater than or equal to 150 MPa²√m, greater than or equal to 200 MPa²√m, greater than or equal to 250 MPa²√m, greater than or equal to 300 MPa²√m, greater than or equal to 350 MPa²√m, greater than or equal to 400 MPa²√m, or even greater than or equal to 450 MPa²√m. In general, the glass-based article will exhibit better fracture resistance and drop performance as the K_1C×CT increases.

In embodiments, the glass-based article is strengthened by ion exchange and the glass-based article comprises a compressive stress region extending from the first surface to a depth of compression and a region of balancing tension in the middle. The tensile stress region may have a maximum CT greater than or equal to 175 MPa and the glass-based article may comprise at least one ion strengthening ion having a mutual diffusivity D into the glass-based article at a temperature of 390° C. of between 300 μm²/hour and 1500 μm²/hour or even between 100 μm²/hour and 3000 μm²/hour. The tensile stress region may have a maximum CT greater than or equal to 175 MPa, and the glass-based article may comprise at least one strengthening ion having a mutual diffusivity D into the glass-based article at a temperature of 430° C. of between 800 μm²/hour and 3500 μm²/hour or even between 100 μm²/hour and 3000 μm²/hour. For example, the diffusivity D may range from greater than or equal to 300 μm²/hour to less than or equal to 3500 μm²/hour, from greater than or equal to 400 μm²/hour to less than or equal to 3000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 2500 μm²/hour, from greater than or equal to 600 μm²/hour to less than or equal to 2000 μm²/hour, from greater than or equal to 700 μm²/hour to less than or equal to 1800 μm²/hour, from greater than or equal to 800 μm²/hour to less than or equal to 1600 μm²/hour, from greater than or equal to 900 μm²/hour to less than or equal to 1600 μm²/hour, from greater than or equal to 1000 μm²/hour to less than or equal to 2000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 1500 μm²/hour, from greater than or equal to 100 μm²/hour to less than or equal to 5000 μm²/hour, from greater than or equal to 100 μm²/hour to less than or equal to 4000 μm²/hour, from greater than or equal to 100 μm²/hour to less than or equal to 3000 μm²/hour, from greater than or equal to 100 μm²/hour to less than or equal to 2000 μm²/hour, from greater than or equal to 100 μm²/hour to less than or equal to 1500 μm²/hour, from greater than or equal to 200 μm²/hour to less than or equal to 5000 μm²/hour, from greater than or equal to 200 μm²/hour to less than or equal to 4000 μm²/hour, from greater than or equal to 200 μm²/hour to less than or equal to 3000 μm²/hour, from greater than or equal to 200 μm²/hour to less than or equal to 2000 μm²/hour, from greater than or equal to 200 μm²/hour to less than or equal to 1500 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 5000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 4000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 3000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 2000 μm²/hour, from greater than or equal to 500 μm²/hour to less than or equal to 1500 μm²/hour, from greater than or equal to 1000 μm²/hour to less than or equal to 5000 μm²/hour, from greater than or equal to 1000 μm²/hour to less than or equal to 4000 μm²/hour, from greater than or equal to 1000 μm²/hour to less than or equal to 3000 μm²/hour, from greater than or equal to 1000 μm²/hour to less than or equal to 2000 μm²/hour, or even from greater than or equal to 1000 μm²/hour to less than or equal to 1500 μm²/hour. It should be understood that the diffusivity may be within a range formed from any one of the lower bounds for diffusivity and any one of the upper bounds for the diffusivity described herein.

In the same or different embodiments, the arithmetic product of the maximum CT and the diffusivity may be greater than or equal to 50,000 MPa·μm²/hour, or greater than or equal to 60,000 MPa·μm²/hour, or greater than or equal to 70,000 MPa·μm²/hour, or greater than or equal to 80,000 MPa·μm²/hour, or greater than or equal to 90,000 MPa·μm²/hour, or greater than or equal to 100,000 MPa·μm²/hour, or greater than or equal to 200,000 MPa·μm²/hour, or greater than or equal to 400,000 MPa·μm²/hour, or greater than or equal to 600,000 MPa·μm²/hour, or greater than or equal to 800,000 MPa·μm²/hour, or greater than or equal to 1,000,000 MPa·μm²/hour, or greater than or equal to 1,200,000 MPa·μm²/hour, or even greater than or equal to 1,400,000 MPa·μm²/hour. Without intending to be bound by any particular theory, it is believed that a high diffusivity may be desirable for faster ion exchange and greater throughput. However, the high diffusivity could potentially be associated with lower CT. Thus, it is believed that the arithmetic product of the maximum CT and the diffusivity provides an indication of merit for cost and performance.

In embodiments, the glass-based article may comprise a composition comprising SiO₂, Li₂O, Ta₂O₅, and Al₂O₃. The Al₂O₃content may be greater than or equal to 16 mol. %. The glass-based article may be strengthened by ion exchange and the glass-based article may comprise a compressive stress region extending from a first surface of the glass-based article to a depth of compression, and a tensile stress region extending from the depth of compression toward a second surface opposite the first surface. This tensile stress region may have a maximum central tension greater than or equal to 160 MPa. For example, the Al₂O₃content may be greater than or equal to 18 mol. % or even greater than or equal to 20 mol. %.

EXAMPLES

The embodiments described herein will be further clarified by the following examples.

The compositions were formed by mixing a batch of glass raw materials (e.g., powders of SiO₂, Al₂O₃, alkali carbonates, nitrates, or sulfates, alkaline earth carbonates, nitrates, sulfates, or oxides, and the like, as provided in Tables 1A-1U) such that the batch of glass raw materials has the desired composition. Thereafter, the batch of glass raw materials were heated to form a molten composition and then poured into a bucket of water to create cullet. This cullet was then remelted at a slightly higher temperature to remove bubbles. This double melting procedure improves the quality and homogeneity of the resulting glass for laboratory scale melting. The molten glass was then poured onto a steel table and allowed to set before it was placed in an annealer at approximately the anneal point of the glass to remove stress. The glass was then cooled to room temperature and cut and polished into samples for measurement.

TABLE 1A

Sample/mol %
1
2
3
4
5
6
7

SiO₂
58.811
67.679
60.260
60.410
62.196
63.894
68.640

Al₂O₃
19.113
9.445
17.106
19.295
16.417
16.760
17.076

B₂O₃
6.022
3.979
6.829
3.996
5.094
3.053

P₂O₅

0.003
0.027

Li₂O
15.921
13.682
8.280
11.748
7.999
7.991
9.904

Na₂O
0.017
0.088
2.365
1.386
0.990
1.010
1.054

K₂O

0.027
0.032
0.036
0.003
0.004
0.026

MgO
0.016
0.027
1.005
0.035
2.521
1.001
0.028

CaO
0.011
0.049
0.046
0.027
0.514
1.019
0.025

SrO

0.018
0.008

SnO₂
0.074
0.074
0.071
0.072
0.102
0.106
0.067

ZrO₂

0.001

TiO₂

0.006
0.007

0.504
0.509
0.009

Fe₂O₃

0.016
0.020
0.021
0.006
0.006
0.016

ZnO

1.010

Ta₂O₅

4.912

Y₂O₃

3.945
2.967
3.622
1.836
3.147

La₂O₃

0.001

1.785

R₂O
15.937
13.797
10.677
13.170
8.991
9.005
10.984

RO
0.027
0.077
1.051
0.062
3.053
2.027
0.052

R₂O + R′O-
−3.149
−0.490
0.532
−1.612
0.556
−0.805
−1.329

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−3.176
−0.560
−6.428
−6.125
−7.426
−7.755
−6.092

Ta₂O₅

R₂O + R′O-
−3.149
−0.484
−5.378
−6.062
−4.373
−5.728
−6.040

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.999
0.992
0.775
0.892
0.890
0.887
0.902

Li₂O/(Al₂O₃+
0.833
0.953
0.484
0.609
0.487
0.477
0.580

Ta₂O₅)

TABLE 1B

Sample/mol %
8
9
10
11
12
13
14

SiO₂
55.127
65.378
69.769
67.304
67.430
62.137
67.480

Al₂O₃
22.344
17.318
16.433
17.740
17.250
16.478
17.763

B₂O₃
6.096
1.996

5.089

P₂O₅

Li₂O
16.320
9.537
9.600
9.446
9.564
8.009
10.221

Na₂O

2.308
1.003
2.060
2.307
0.975
1.085

K₂O

0.026
0.025
0.027
0.026
0.004
0.026

MgO
0.023
0.028
0.024
0.026
0.028
2.530
0.028

CaO
0.010
0.024
0.023
0.024
0.024
0.516
0.025

SrO

0.008

SnO₂
0.075
0.073
0.063
0.069
0.069
0.108
0.070

ZrO₂

TiO₂

0.008
0.008
0.009
0.009
0.510
0.008

Fe₂O₃

0.016
0.016
0.017
0.017
0.006
0.017

ZnO

0.001

Ta₂O₅

Y₂O₃

3.279
3.029
3.271
3.269
1.841
3.271

La₂O₃

1.780

R₂O
16.320
11.871
10.628
11.532
11.896
8.988
11.332

RO
0.033
0.052
0.048
0.050
0.052
3.054
0.053

R₂O + R′O-
−5.991
−0.485
−1.223
−1.260
−0.408
0.487
−1.480

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−6.024
−5.447
−5.806
−6.208
−5.354
−7.489
−6.430

Ta₂O₅

R₂O + R′O-
−5.991
−5.395
−5.758
−6.158
−5.302
−4.436
−6.378

Al₂O₃-Ta₂O₅

Li₂O/R₂O
1.000
0.803
0.903
0.819
0.804
0.891
0.902

Li₂O/(Al₂O₃+
0.730
0.551
0.584
0.532
0.554
0.486
0.575

Ta₂O₅)

TABLE 1C

Sample/mol %
15
16
17
18
19
20
21

SiO₂
61.987
62.298
60.710
64.320
60.039
62.075
64.220

Al₂O₃
19.915
19.332
19.301
19.357
19.799
20.251
19.403

B₂O₃

1.969
2.434

3.864

P₂O₅

0.025

Li₂O
12.035
11.844
11.535
11.764
15.871
13.992
11.811

Na₂O
1.876
1.389
1.674
1.387
0.171
1.871
1.369

K₂O
0.038
0.036
0.057
0.036
0.039
0.039
0.035

MgO
3.966
0.038
0.039
0.031
0.029
0.030
0.032

CaO
0.071
0.026
0.037
0.029
0.050
0.049
0.030

SrO

SnO₂
0.080
0.072
0.071
0.072
0.079
0.075
0.077

ZrO₂

TiO₂

Fe₂O₃
0.025
0.021
0.030
0.021
0.024
0.023
0.022

ZnO

Ta₂O₅

Y₂O₃
0.001
2.966
4.102
2.974

1.587
2.008

La₂O₃

0.001

0.001

0.984

R₂O
13.949
13.269
13.267
13.186
16.081
15.901
13.216

RO
4.037
0.064
0.077
0.060
0.079
0.079
0.062

R₂O + R′O-
−1.928
−1.548
0.195
−1.647
−3.638
−1.889
−1.638

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−5.966
−6.062
−6.034
−6.170
−3.717
−4.349
−6.188

Ta₂O₅

R₂O + R′O-
−1.929
−5.998
−5.958
−6.110
−3.638
−4.270
−6.126

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.863
0.893
0.869
0.892
0.987
0.880
0.894

Li₂O/(Al₂O₃+
0.604
0.613
0.598
0.608
0.802
0.691
0.609

Ta₂O₅)

TABLE 1D

Sample/mol %
22
23
24
25
26
27
28

SiO₂
62.207
66.498
67.985
62.259
63.276
62.016
65.005

Al₂O₃
20.615
18.838
8.530
19.915
18.482
19.883
19.149

B₂O₃

1.925

P₂O₅

0.007

Li₂O
11.969
8.562
15.657
15.471
11.250
14.026
11.383

Na₂O
1.848
0.092
0.106
0.147
0.724
1.875
0.134

K₂O
0.040
0.042
0.038
0.047
0.058
0.039
0.041

MgO
0.031
0.032
0.036
2.000
0.030
1.993
0.030

CaO
0.049
0.034
0.060
0.045
0.040
0.058
0.035

SrO

SnO₂
0.070
0.069
0.074
0.078
0.067
0.077
0.069

ZrO₂

0.995

TiO₂

0.005
0.007
0.004

Fe₂O₃
0.023
0.023
0.021
0.027
0.028
0.024
0.022

ZnO

Ta₂O₅

6.473

Y₂O₃
3.138
5.788

4.111
0.001
4.122

La₂O₃

R₂O
13.856
8.696
15.800
15.665
12.032
15.940
11.558

RO
0.081
0.065
0.096
2.045
0.070
2.052
0.065

R₂O + R′O-
−1.972
−1.400
−0.109
−2.209
−0.214
−1.891
−1.344

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−6.759
−10.142
0.797
−4.250
−6.450
−3.944
−7.591

Ta₂O₅

R₂O + R′O-
−6.679
−10.077
0.893
−2.205
−6.380
−1.892
−7.526

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.864
0.985
0.991
0.988
0.935
0.880
0.985

Li₂O/(Al₂O₃+
0.581
0.455
1.044
0.777
0.609
0.705
0.594

Ta₂O₅)

TABLE 1E

Sample/mol %
29
30
31
32
33
34
35

SiO₂
64.873
65.670
64.170
62.747
63.393
64.737
62.114

Al₂O₃
12.941
19.068
19.451
19.158
20.823
17.942
20.443

B₂O₃
5.952

P₂O₅

0.029

Li₂O
16.128
10.281
11.811
12.038
15.377
11.087
12.990

Na₂O
0.001
0.101
1.367
1.700
0.144
1.559
1.862

K₂O
0.001
0.043
0.036
0.059
0.043
0.044
0.040

MgO
0.012
0.034
0.025
0.030
0.030
2.089
0.029

CaO
0.011
0.034
0.031
0.040
0.051
0.060
0.050

SrO

SnO₂
0.076
0.068
0.078
0.069
0.078
0.097
0.071

ZrO₂

TiO₂

0.005

Fe₂O₃

0.022
0.022
0.029
0.024
0.026
0.023

ZnO

Ta₂O₅

Y₂O₃

4.655
1.022
4.115

2.351
2.368

La₂O₃

1.979

R₂O
16.130
10.425
13.214
13.797
15.565
12.690
14.893

RO
0.023
0.068
0.056
0.070
0.081
2.148
0.079

R₂O + R′O-
3.212
−1.597
−1.680
0.882
−5.177
0.423
−1.919

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
3.188
−8.643
−6.237
−5.360
−5.258
−5.252
−5.550

Ta₂O₅

R₂O + R′O-
3.212
−8.575
−6.182
−5.290
−5.177
−3.104
−5.471

Al₂O₃-Ta₂O₅

Li₂O/R₂O
1.000
0.986
0.894
0.872
0.988
0.874
0.872

Li₂O/(Al₂O₃+
1.246
0.539
0.607
0.628
0.738
0.618
0.635

Ta₂O₅)

TABLE 1F

Sample/mol %
36
37
38
39
40
41
42

SiO₂
62.309
67.172
59.972
62.144
66.226
64.902
67.716

Al₂O₃
17.952
17.866
19.784
19.928
16.015
19.307
10.551

B₂O₃
2.024

2.004

P₂O₅
1.948

0.025

0.026

0.006

Li₂O
15.372
11.359
15.845
15.595
15.336
11.940
15.575

Na₂O
0.177
0.128
0.163
2.107
0.176
0.111
0.109

K₂O
0.040
0.036
0.040
0.048
0.039
0.041
0.038

MgO
0.024
0.023
3.989
0.029
0.022
0.032
0.031

CaO
0.048
0.034
0.073
0.032
0.047
0.034
0.056

SrO

SnO₂
0.076
0.065
0.077
0.079
0.077
0.072
0.074

ZrO₂

0.001

TiO₂

0.005

0.005
0.005

Fe₂O₃
0.024
0.021
0.025
0.026
0.024
0.023
0.021

ZnO

Ta₂O₅

5.806

Y₂O₃

3.275

3.520

La₂O₃

R₂O
15.589
11.524
16.047
17.750
15.552
12.091
15.722

RO
0.072
0.056
4.063
0.061
0.069
0.066
0.086

R₂O + R′O-
−2.291
−1.373
0.326
−2.122
−0.394
−1.875
−0.555

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−2.363
−6.342
−3.737
−2.178
−0.463
−7.216
−0.635

Ta₂O₅

R₂O + R′O-
−2.291
−6.286
0.326
−2.117
−0.394
−7.150
−0.549

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.986
0.986
0.987
0.879
0.986
0.988
0.991

Li₂O/(Al₂O₃+
0.856
0.636
0.801
0.783
0.958
0.618
0.952

Ta₂O₅)

TABLE 1G

Sample/mol %
43
44
45
46
47
48
49

SiO₂
64.149
63.875
61.952
56.390
73.673
63.929
63.779

Al₂O₃
17.929
19.491
15.735
21.766
8.867
19.786
20.330

B₂O₃

6.021

P₂O₅
1.989

0.031
0.002
0.025
0.028

Li₂O
13.816
13.944
16.184
17.506
12.741
13.910
15.481

Na₂O
1.882
0.114
0.001
0.178
0.089
2.114
0.151

K₂O
0.048
0.042
0.001
0.047
0.022
0.040
0.040

MgO
0.039
0.030
0.014
3.840
0.023
0.029
0.032

CaO
0.028
0.032
0.010
0.066
0.042
0.048
0.049

SrO

SnO₂
0.081
0.073
0.077
0.103
0.074
0.079
0.080

ZrO₂

0.004

TiO₂
0.006
0.005

0.006
0.007

Fe₂O₃
0.027
0.022

0.028
0.014
0.023
0.024

ZnO

0.002

Ta₂O₅

4.429

Y₂O₃

2.357

La₂O₃

R₂O
15.746
14.100
16.185
17.731
12.852
16.064
15.672

RO
0.067
0.062
0.024
3.906
0.065
0.077
0.081

R₂O + R′O-
−2.121
−1.798
0.474
−0.134
−0.390
−3.644
−4.577

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−2.182
−5.391
0.450
−4.034
−0.444
−3.722
−4.658

Ta₂O₅

R₂O + R′O-
−2.115
−5.329
0.474
−0.128
−0.379
−3.644
−4.577

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.877
0.989
1.000
0.987
0.991
0.866
0.988

Li₂O/(Al₂O₃+
0.771
0.715
1.028
0.804
0.958
0.703
0.761

Ta₂O₅)

TABLE 1H

Sample/mol %
50
51
52
53
54
55
56

SiO₂
67.722
61.195
62.555
64.263
64.628
64.149
60.325

Al₂O₃
11.522
18.545
15.206
16.019
19.267
19.509
21.884

B₂O₃

3.914
6.120
4.011

P₂O₅
0.008

0.026

0.028

Li₂O
15.570
11.261
15.992
15.281
10.255
11.823
17.384

Na₂O
0.121
0.722
0.022
0.182
2.087
1.353
0.152

K₂O
0.038
0.057

0.039
0.042
0.036
0.039

MgO
0.031
0.027
0.012
0.025
0.032
0.018
0.030

CaO
0.056
0.040
0.011
0.047
0.032
0.032
0.051

SrO

SnO₂
0.076
0.069
0.074
0.076
0.070
0.082
0.077

ZrO₂

TiO₂
0.006

Fe₂O₃
0.020
0.028

0.024
0.022
0.022
0.024

ZnO

Ta₂O₅
4.818

Y₂O₃

4.133

3.547
0.010

La₂O₃

2.956

R₂O
15.729
12.039
16.014
15.502
12.384
13.212
17.574

RO
0.088
0.067
0.024
0.072
0.064
0.050
0.081

R₂O + R′O-
−0.530
−0.240
0.831
−0.445
−1.499
−1.796
−4.229

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−0.612
−6.506
0.807
−0.517
−6.883
−6.296
−4.310

Ta₂O₅

R₂O + R′O-
−0.524
−6.440
0.831
−0.445
−6.819
−6.246
−4.229

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.990
0.935
0.999
0.986
0.828
0.895
0.989

Li₂O/(Al₂O₃+
0.953
0.607
1.052
0.954
0.532
0.606
0.794

Ta₂O₅)

TABLE 1I

Sample/mol %
57
58
59
60
61
62
63

SiO₂
65.103
66.815
63.706
64.095
60.942
63.118
63.972

Al₂O₃
18.533
11.304
20.444
18.978
16.762
19.733
19.849

B₂O₃

6.023

6.015

P₂O₅

0.028
0.030

Li₂O
11.266
15.724
15.447
13.813
16.165
15.619
15.739

Na₂O
0.735
0.027
0.145
2.858
0.003
0.121
0.153

K₂O
0.058

0.041
0.049

0.041
0.053

MgO
0.030
0.009
0.030
0.032
0.017
0.033
0.029

CaO
0.040
0.011
0.050
0.029
0.011
0.032
0.057

SrO

SnO₂
0.071
0.074
0.078
0.078
0.078
0.074
0.110

ZrO₂

TiO₂

0.005

0.005

Fe₂O₃
0.029
0.001
0.024
0.027

0.022
0.031

ZnO

Ta₂O₅

Y₂O₃
4.127

1.190
0.001

La₂O₃

R₂O
12.058
15.752
15.633
16.719
16.168
15.781
15.945

RO
0.070
0.020
0.080
0.061
0.028
0.064
0.086

R₂O + R′O-
−0.214
4.468
−4.731
−2.203
−0.566
−2.107
−3.816

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−6.475
4.448
−4.811
−2.259
−0.594
−3.952
−3.904

Ta₂O₅

R₂O + R′O-
−6.405
4.468
−4.731
−2.198
−0.566
−3.887
−3.818

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.934
0.998
0.988
0.826
1.000
0.990
0.987

Li₂O/(Al₂O₃+
0.608
1.391
0.756
0.728
0.964
0.792
0.793

Ta₂O₅)

TABLE 1J

Sample/mol %
64
65
66
67
68
69
70

SiO₂
64.156
62.006
65.660
63.042
56.271
61.960
66.297

Al₂O₃
17.989
19.847
13.563
18.844
23.630
19.771
17.837

B₂O₃
1.972

P₂O₅
0.030

0.008

0.030
1.942

Li₂O
13.738
16.051
15.531
11.577
19.560
15.908
9.662

Na₂O
1.887
1.873
0.121
1.673
0.191
0.186
0.139

K₂O
0.047
0.038
0.037
0.056
0.045
0.039
0.043

MgO
0.037
0.030
0.034
2.486
0.035
0.028
0.026

CaO
0.029
0.045
0.055
0.048
0.058
0.050
0.035

SrO

SnO₂
0.079
0.079
0.074
0.074
0.104
0.079
0.067

ZrO₂

0.001

TiO₂
0.005

0.005

0.005

Fe₂O₃
0.027
0.023
0.020
0.030
0.028
0.023
0.022

ZnO

0.001

Ta₂O₅

4.882

Y₂O₃

0.001

2.162

5.863

La₂O₃

R₂O
15.671
17.962
15.689
13.306
19.796
16.133
9.845

RO
0.065
0.075
0.089
2.534
0.093
0.078
0.060

R₂O + R′O-
−2.257
−1.810
−2.672
0.239
−3.746
−3.559
0.862

Al₂O₃-Ta₂O₅+

1.5*RE₂O₃-

ZrO₂-TiO₂

R₂O-Al₂O₃-
−2.317
−1.885
−2.756
−5.538
−3.834
−3.637
−7.992

Ta₂O₅

R₂O + R′O-
−2.252
−1.810
−2.667
−3.004
−3.741
−3.559
−7.932

Al₂O₃-Ta₂O₅

Li₂O/R₂O
0.877
0.894
0.990
0.870
0.988
0.986
0.981

Li₂O/(Al₂O₃+
0.764
0.809
0.842
0.614
0.828
0.805
0.542

Ta₂O₅)

TABLE 1K

Sample/mol %
71
72
73
74
75
76
77

SiO₂
66.499
63.859
67.648
66.007
68.157
64.184
66.208

Al₂O₃
18.417
19.309
12.056
18.533
16.003
18.962
17.902

B₂O₃

0.004

P₂O₅

0.036
0.005

0.027

0.025

Li₂O
14.422
14.185
14.614
11.714
13.463
13.040
15.456

Na₂O
0.401
2.356
0.109
0.136
0.145
2.603
0.174

K₂O
0.051
0.051
0.032
0.039
0.047
0.048
0.040

MgO
0.029
0.028
0.032
0.024
1.999
0.056
0.022

CaO
0.047
0.055
0.051
0.034
0.041
0.987
0.049

SrO

SnO₂
0.100
0.076
0.074
0.067
0.076
0.082
0.077

ZrO₂

0.001

TiO₂

0.008
0.003

0.003
0.005

Fe₂O₃
0.029
0.030
0.018
0.021
0.026
0.027
0.023

ZnO

0.001

Ta₂O₅

5.345

Y₂O₃
0.001
0.001

3.401

La₂O₃

R₂O
14.873
16.591
14.754
11.889
13.655
15.691
15.671

RO
0.076
0.082
0.083
0.058
2.041
1.043
0.071

R₂O + R′O −
−3.467
−2.641
−2.568
−1.484
−0.310
−2.232
−2.161

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−3.544
−2.718
−2.647
−6.645
−2.347
−3.271
−2.232

Ta₂O₅

R₂O + R′O −
−3.468
−2.635
−2.564
−6.586
−0.307
−2.227
−2.161

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.970
0.855
0.990
0.985
0.986
0.831
0.986

Li₂O/(Al₂O₃+
0.783
0.735
0.840
0.632
0.841
0.688
0.863

Ta₂O₅)

TABLE 1L

Sample/mol %
78
79
80
81
82
83
84

SiO₂
56.465
64.057
58.297
68.178
62.436
62.204
63.150

Al₂O₃
22.874
20.040
21.842
7.983
20.831
19.899
19.502

B₂O₃

P₂O₅
0.027

0.030

0.029
0.030

Li₂O
20.249
15.826
15.492
15.834
16.335
15.494
11.290

Na₂O
0.154

0.140

0.143
0.140
1.696

K₂O
0.039

0.049

0.042
0.049
0.057

MgO
0.027

0.033

0.027
0.032
0.030

CaO
0.052

0.042

0.050
0.035
0.042

SrO

3.961

2.000

SnO₂
0.078
0.077
0.073
0.071
0.077
0.077
0.070

ZrO₂

TiO₂

Fe₂O₃
0.024

0.026

0.024
0.026
0.028

ZnO

Ta₂O₅

7.934

Y₂O₃

4.125

La₂O₃

R₂O
20.443
15.826
15.680
15.834
16.519
15.683
13.043

RO
0.079

4.036

0.078
2.067
0.073

R₂O + R′O −
−2.352
−4.214
−2.126
−0.083
−4.234
−2.150
−0.199

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−2.432
−4.214
−6.162
−0.083
−4.312
−4.216
−6.459

Ta₂O₅

R₂O + R′O −
−2.352
−4.214
−2.126
−0.083
−4.234
−2.150
−6.387

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.991
1.000
0.988
1.000
0.989
0.988
0.866

Li₂O/(Al₂O₃+
0.885
0.790
0.709
0.995
0.784
0.779
0.579

Ta₂O₅)

TABLE 1M

Sample/mol %
85
86
87
88
89
90
91

SiO₂
64.277
50.487
62.455
65.248
60.398
71.690
61.221

Al₂O₃
18.977
25.718
20.004
18.855
20.915
9.431
20.471

B₂O₃

P₂O₅

0.028

0.026
0.028
0.004

Li₂O
12.187
23.369
17.197
15.472
18.287
13.649
11.235

Na₂O
2.363
0.162
0.124
0.175
0.143
0.091
0.726

K₂O
0.049
0.040
0.039
0.041
0.040
0.028
0.056

MgO
0.069
0.035
0.030
0.025
0.030
0.023
1.998

CaO
1.959
0.054
0.031
0.050
0.051
0.048
0.053

SrO

SnO₂
0.080
0.077
0.080
0.076
0.077
0.074
0.069

ZrO₂

0.001

0.004

TiO₂
0.005

0.005

0.005

Fe₂O₃
0.028
0.024
0.022
0.023
0.024
0.016
0.029

ZnO

Ta₂O₅

4.926

Y₂O₃

0.001

4.132

La₂O₃

R₂O
14.598
23.571
17.361
15.688
18.470
13.767
12.017

RO
2.028
0.089
0.061
0.076
0.081
0.071
2.050

R₂O + R′O −
−2.357
−2.058
−2.587
−3.091
−2.363
−0.528
−0.206

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−4.379
−2.147
−2.643
−3.166
−2.444
−0.590
−8.454

Ta₂O₅

R₂O + R′O −
−2.351
−2.058
−2.582
−3.091
−2.363
−0.519
−6.404

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.835
0.991
0.991
0.986
0.990
0.991
0.935

Li₂O/(Al₂O₃+
0.642
0.909
0.860
0.821
0.874
0.951
0.549

Ta₂O₅)

TABLE 1N

Sample/mol %
92
93
94
95
96
97
98

SiO₂
58.314
66.391
64.306
58.210
69.720
63.884
62.240

Al₂O₃
21.899
13.848
17.997
21.863
9.441
19.848
19.895

B₂O₃

2.003

P₂O₅

0.030
0.003
0.026
1.985

Li₂O
15.437
15.725
13.638
15.515
13.659
11.944
15.491

Na₂O
0.140

2.852
0.286
0.099
4.068
0.160

K₂O
0.048

0.048
0.047
0.028
0.040
0.047

MgO
3.989

0.051
0.033
0.025
0.028
0.029

CaO
0.058

0.990
0.035
0.046
0.050
0.033

SrO

0.001

SnO₂
0.078
0.072
0.078
0.076
0.074
0.077
0.078

ZrO₂

0.001

0.001

TiO₂
0.003

0.005

0.005

Fe₂O₃
0.028

0.027
0.026
0.016
0.024
0.026

ZnO

3.863

Ta₂O₅

3.964

4.868

Y₂O₃

La₂O₃

R₂O
15.625
15.725
16.538
15.847
13.786
16.052
15.699

RO
4.047

1.041
0.069
0.072
0.078
0.062

R₂O + R′O −
−2.230
−2.087
−0.423
−5.947
−0.457
−3.719
−4.135

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−6.274
−2.087
−1.459
−6.016
−0.523
−3.796
−4.196

Ta₂O₅

R₂O + R′O −
−2.227
−2.087
−0.418
−5.947
−0.451
−3.719
−4.134

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.988
1.000
0.825
0.979
0.991
0.744
0.987

Li₂O/(Al₂O₃+
0.705
0.883
0.758
0.710
0.955
0.602
0.779

Ta₂O₅)

TABLE 1O

Sample/mol %
99
100
101
102
103
104
105

SiO₂
68.763
64.172
62.137
62.235
58.341
72.009
65.152

Al₂O₃
8.001
17.799
19.890
19.917
21.896
15.898
16.946

B₂O₃

P₂O₅

0.046
0.030

0.028
1.987

Li₂O
15.242
17.501
15.561
15.502
15.473
11.719
13.794

Na₂O
0.111
0.167
0.223
0.153
4.056
0.129
1.895

K₂O

0.044
0.048
0.048
0.050
0.041
0.048

MgO
0.028
0.037
0.026
0.065
0.032
0.024
0.036

CaO

0.069
0.033
1.962
0.035
0.045
0.028

SrO

0.001

SnO₂
0.070
0.103
0.078
0.080
0.078
0.076
0.076

ZrO₂

0.001
0.001

TiO₂

0.004

0.004
0.003

0.005

Fe₂O₃

0.029
0.026
0.027
0.026
0.024
0.027

ZnO

1.935

Ta₂O₅
7.785

Y₂O₃

La₂O₃

R₂O
15.353
17.712
15.832
15.703
19.579
11.889
15.737

RO
0.028
0.107
0.060
2.027
0.067
0.069
0.063

R₂O + R′O −
−0.404
0.015
−3.999
−2.191
−2.253
−3.940
−1.150

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−0.433
−0.088
−4.058
−4.214
−2.317
−4.009
−1.209

Ta₂O₅

R₂O + R′O −
−0.404
0.019
−3.999
−2.186
−2.250
−3.940
−1.145

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.993
0.988
0.983
0.987
0.790
0.986
0.877

Li₂O/(Al₂O₃+
0.966
0.983
0.782
0.778
0.707
0.737
0.814

Ta₂O₅)

TABLE 1P

Sample/mol %
106
107
108
109
110
111
112

SiO₂
56.302
69.841
58.452
66.063
56.435
64.262
64.517

Al₂O₃
21.744
10.004
19.887
17.946
19.864
17.970
18.772

B₂O₃

2.035
0.004

P₂O₅
0.031
0.006
3.864
0.027
0.031
0.031
1.989

Li₂O
19.530
14.640
15.349
13.799
19.347
15.520
14.342

Na₂O
0.184
0.107
0.187
1.933
0.176
0.158
0.149

K₂O
0.048
0.033
0.042
0.048
0.046
0.049
0.044

MgO
1.925
0.032
0.025
0.030
3.858
0.027
0.029

CaO
0.063
0.050
0.051
0.033
0.067
0.032
0.050

SrO

0.002

SnO₂
0.104
0.073
0.077
0.078
0.105
0.073
0.077

ZrO₂

0.001

1.822

TiO₂
0.006
0.004

0.004
0.005

Fe₂O₃
0.028
0.019
0.024
0.026
0.028
0.027
0.024

ZnO
0.002

0.001
0.002

Ta₂O₅

5.178

Y₂O₃

La₂O₃

R₂O
19.762
14.780
15.578
15.780
19.569
15.727
14.535

RO
1.988
0.082
0.076
0.063
3.925
0.061
0.080

R₂O + R′O −
0.001
−0.325
−4.234
−2.107
3.625
−4.004
−4.158

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−1.983
−0.402
−4.309
−2.166
−0.295
−2.243
−4.237

Ta₂O₅

R₂O + R′O −
0.006
−0.320
−4.234
−2.103
3.630
−2.181
−4.158

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.988
0.991
0.985
0.874
0.989
0.987
0.987

Li₂O/(Al₂O₃+
0.898
0.964
0.772
0.769
0.974
0.864
0.764

Ta₂O₅)

TABLE 1Q

Sample/mol %
113
114
115
116
117
118
119

SiO₂
50.564
62.341
72.245
62.196
60.456
56.429
75.961

Al₂O₃
24.785
19.973
13.946
17.905
17.970
21.792
11.963

B₂O₃

3.989

P₂O₅
0.029

0.046
3.951
1.955
3.933
0.044

Li₂O
24.226
13.636
13.297
13.835
15.234
17.467
11.594

Na₂O
0.161
2.842
0.157
1.887
0.179
0.153
0.141

K₂O
0.040
0.049
0.044
0.048
0.040
0.039
0.042

MgO
0.033
0.053
0.031
0.035
0.023
0.030
0.029

CaO
0.054
0.988
0.068
0.028
0.049
0.049
0.063

SrO

SnO₂
0.077
0.080
0.103
0.077
0.076
0.077
0.102

ZrO₂

0.001

0.001

TiO₂

0.005
0.005
0.005

0.005

Fe₂O₃
0.023
0.027
0.030
0.026
0.024
0.024
0.029

ZnO

0.001

Ta₂O₅

Y₂O₃

La₂O₃

R₂O
24.427
16.526
13.498
15.770
15.452
17.659
11.777

RO
0.087
1.041
0.099
0.062
0.072
0.079
0.092

R₂O + R′O −
−0.270
−2.411
−0.354
−2.078
−2.445
−4.053
−0.100

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−0.358
−3.446
−0.447
−2.135
−2.517
−4.132
−0.186

Ta₂O₅

R₂O + R′O −
−0.270
−2.406
−0.348
−2.073
−2.445
−4.053
−0.094

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.992
0.825
0.985
0.877
0.986
0.989
0.984

Li₂O/(Al₂O₃+
0.977
0.683
0.953
0.773
0.848
0.802
0.969

Ta₂O₅)

TABLE 1R

Sample/mol %
120
121
122
123
124
125
126

SiO₂
64.192
56.220
62.292
66.224
72.113
64.946
64.321

Al₂O₃
16.965
21.717
18.961
14.044
14.932
16.873
17.778

B₂O₃

2.036

P₂O₅

0.031

0.026
0.028
1.950
3.945

Li₂O
13.793
21.536
13.701
15.284
12.592
14.083
13.579

Na₂O
2.854
0.187
2.851
0.184
0.121
1.898
0.149

K₂O
0.048
0.047
0.049
0.040
0.040
0.051
0.041

MgO
0.072
0.031
0.069
1.994
0.022
0.026
0.030

CaO
1.956
0.057
1.959
0.058
0.043
0.053
0.047

SrO

SnO₂
0.078
0.104
0.078
0.078
0.079
0.074
0.079

ZrO₂

TiO₂
0.005
0.006
0.004

0.007

Fe₂O₃
0.027
0.028
0.028
0.024
0.024
0.030
0.024

ZnO

0.002

Ta₂O₅

Y₂O₃

0.001

La₂O₃

R₂O
16.695
21.771
16.601
15.508
12.753
16.032
13.769

RO
2.028
0.089
2.027
2.052
0.064
0.079
0.076

R₂O + R′O −
1.754
0.137
−0.337
3.516
−2.114
−0.768
−3.933

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−0.269
0.054
−2.360
1.463
−2.179
−0.841
−4.009

Ta₂O₅

R₂O + R′O −
1.759
0.142
−0.333
3.516
−2.114
−0.762
−3.933

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.826
0.989
0.825
0.986
0.987
0.878
0.986

Li₂O/(Al₂O₃+
0.813
0.992
0.723
1.088
0.843
0.835
0.764

Ta₂O₅)

TABLE 1S

Sample/mol %
127
128
129
130
131
132
133

SiO₂
60.209
59.997
58.310
60.204
62.342
63.788
60.041

Al₂O₃
15.916
19.736
21.881
19.782
18.920
19.764
19.786

B₂O₃

0.004

P₂O₅
0.032
3.860

0.045
1.948

Li₂O
19.563
15.989
15.485
19.480
12.649
15.940
15.731

Na₂O
0.159
0.188
0.145
0.174
3.893
0.168
0.159

K₂O
0.047
0.039
0.051
0.042
0.051
0.067
0.061

MgO
3.839
0.032
0.109
0.037
0.030
0.030
3.960

CaO
0.065
0.049
3.898
0.071
0.035
0.050
0.074

SrO

SnO₂
0.104
0.079
0.079
0.103
0.076
0.100
0.100

ZrO₂

0.001
0.005

0.001

TiO₂
0.006

0.004
0.003
0.003

Fe₂O₃
0.027
0.024
0.029
0.029
0.026
0.029
0.028

ZnO
0.004

0.001
0.001

Ta₂O₅

Y₂O₃

La₂O₃

R₂O
19.769
16.217
15.681
19.696
16.593
16.174
15.950

RO
3.904
0.081
4.007
0.108
0.065
0.081
4.034

R₂O + R′O −
7.751
−3.438
−2.197
0.019
−2.270
−3.510
0.197

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
3.854
−3.519
−6.200
−0.086
−2.328
−3.590
−3.836

Ta₂O₅

R₂O + R′O −
7.758
−3.438
−2.193
0.022
−2.262
−3.510
0.198

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.990
0.986
0.988
0.989
0.762
0.985
0.986

Li₂O/(Al₂O₃+
1.229
0.810
0.708
0.985
0.669
0.806
0.795

Ta₂O₅)

TABLE 1T

Sample/mol %
134
135
136
137
138
139
140

SiO₂
70.126
65.218
67.175
64.304
68.207
58.322
64.204

Al₂O₃
15.959
17.890
16.907
17.805
15.901
21.878
15.920

B₂O₃

0.004

P₂O₅
0.028
0.990
0.025
1.952
1.992
0.031
3.947

Li₂O
13.537
15.486
15.486
15.524
13.549
13.656
13.806

Na₂O
0.130
0.184
0.182
0.189
0.131
5.874
1.894

K₂O
0.040
0.040
0.040
0.043
0.040
0.049
0.048

MgO
0.027
0.019
0.025
0.024
0.026
0.031
0.036

CaO
0.045
0.048
0.047
0.050
0.046
0.039
0.027

SrO

SnO₂
0.078
0.077
0.078
0.078
0.078
0.077
0.079

ZrO₂

TiO₂

0.003
0.006

Fe₂O₃
0.025
0.023
0.023
0.023
0.024
0.026
0.026

ZnO

0.001

Ta₂O₅

Y₂O₃

La₂O₃

R₂O
13.707
15.709
15.708
15.756
13.720
19.579
15.748

RO
0.072
0.067
0.072
0.074
0.072
0.070
0.063

R₂O + R′O −
−2.180
−2.113
−1.126
−1.975
−2.109
−2.232
−0.114

Al₂O₃− Ta₂O₅+

1.5*RE₂O₃− ZrO₂−

TiO₂

R₂O − Al₂O₃−
−2.252
−2.180
−1.198
−2.049
−2.180
−2.299
−0.172

Ta₂O₅

R₂O + R′O −
−2.180
−2.113
−1.126
−1.975
−2.109
−2.229
−0.109

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.988
0.986
0.986
0.985
0.988
0.697
0.877

Li₂O/(Al₂O₃+
0.848
0.866
0.916
0.872
0.852
0.624
0.867

Ta₂O₅)

TABLE 1U

Sample/mol %
141
142
143
144
145

SiO₂
66.205
62.342
70.080
67.950
68.763

Al₂O₃
16.930
19.924
14.904
15.833
8.001

B₂O₃
0.004
0.004

P₂O₅
1.953
0.028
1.987

Li₂O
12.739
13.559
12.685
15.793
15.242

Na₂O
1.925
3.895
0.131
0.168
0.111

K₂O
0.050
0.051
0.039
0.066

MgO
0.032
0.034
0.024
0.031
0.028

CaO
0.036
0.038
0.044
0.057

SrO

SnO₂
0.078
0.077
0.076
0.065
0.070

ZrO₂
0.005

0.001

TiO₂
0.003
0.002

Fe₂O₃
0.026
0.026
0.024
0.031

ZnO
0.001
0.001

Ta₂O₅

Y₂O₃

La2O₃

R₂O
14.714
17.505
12.855
16.028
15.353

RO
0.069
0.072
0.068
0.088
0.028

R₂O + R′O −
−2.155
−2.349
−1.982
0.282
7.380

Al₂O₃− Ta₂O₅+

1.5 * RE₂O₃−

ZrO₂− TiO₂

R₂O − Al₂O₃−
−2.216
−2.419
−2.049
0.195
7.352

Ta₂O₅

R₂O + R′O −
−2.147
−2.347
−1.982
0.283
7.380

Al₂O₃− Ta₂O₅

Li₂O/R₂O
0.866
0.775
0.987
0.985
0.993

Li₂O/(Al₂O₃+
0.752
0.681
0.851
0.998
1.905

Ta₂O₅)

The properties of the compositions were investigated by methods discussed above, and the results are tabulated in Tables 2A-2U. The strain point, anneal point, softening temperature, and liquidus temperature are reported in ° C. CTE is reported in values×10⁻⁷/° C. Density is reported in g/cm³. Liquidus viscosity is reported in kP. K_1Cis reported in MPa√m. The shear modulus and Young's modulus are reported in GPa, while the specific modulus, as the ratio between Young's modulus and the density, is reported in GPa·cm·g⁻¹. Poisson's ratio is unitless. G_1Cis reported in J/m². SOC is reported in nm/cm/MPa. Maximum CT values for both annealed and fictivated glasses are reported in MPa. Further, the ion exchange time required to attain these maximum CT values is reported in hours.

TABLE 2A

Property
1
2
3
4
5
6
7

Avg. CTE (10⁻⁷/C.)
58

52
54.9

49

(20-300° C.)

Strain (° C.)
574
594
614
627
633
634
694

Anneal (° C.)
620
640
660
672
678
680
742

Softening (° C.)
830
843

Density (g/cm³)
2.377
2.907
2.593
2.564
2.601
2.678
2.571

Liquidus
1310
1240
1165
1270
1155
1200
1305

temperature (° C.)

Liquidus viscosity
0.8
2.3
4.9
1.1
9.3
5.0
3.8

(kP)

K_1C(MPa√m)
0.849
0.890
0.880
0.875
0.876
0.869
0.872

Poisson's Ratio
0.231
0.215
0.241
0.237
0.233
0.221
0.226

Shear Modulus
32.27
36.54
35.03
35.58
35.99
36.06
36.47

(GPa)

Young's Modulus
79.36
88.74
86.94
87.98
88.67
88.05
89.36

(GPa)

Specific Modulus
33.39
30.52
33.53
34.31
34.09
32.88
34.76

(GPa · cm³/g)

G_1C(J/m²)
9.08
8.93
8.91
8.70
8.65
8.58
8.51

SOC
30.66
35.08
29.05
28.59
28.7
28.1
28.01

(nm/cm/MPa)

Maximum CT
385
315
177
270
185
195
215

(annealed; MPa)

Time for
64
32
24
24
64
64
20

maximum CT

(annealed, h)

Maximum CT

156

(fictivated; MPa)

Time for

24

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
455
827

270

D 430° C. (um²/hr)
1130
1803
423
770
361
308
1232

D430*CT
435050
567945
74871
207900
66785
60060
264880

(MPa · μm²/hour)

TABLE 2B

Property
8
9
10
11
12
13
14

Avg. CTE (10⁻⁷/C.)
56.8
53.6
48.2
51.5
53.4

49.6

(20-300° C.)

Strain (° C.)
585
657
699
690
685
620
693

Anneal (° C.)
628
705
746
737
732
665
738

Softening (° C.)
824

Density (g/cm³)
2.409
2.573
2.558
2.586
2.583
2.652
2.585

Liquidus
>1460
1245
1300
1285
1265
1165
1305

temperature (° C.)

Liquidus viscosity

5.0
5.5
4.5
5.8
6.1
3.1

(kP)

K_1C(MPa√m)
0.839
0.864
0.864
0.870
0.866
0.856
0.866

Poisson's Ratio
0.235
0.229
0.220
0.227
0.227
0.238
0.227

Shear Modulus
33.51
35.78
36.34
36.61
36.40
35.58
36.75

(GPa)

Young's Modulus
82.74
87.98
88.60
89.84
89.36
88.05
90.18

(GPa)

Specific Modulus
34.34
34.19
34.64
34.74
34.59
33.20
34.89

(GPa · cm³/g)

G_1C(J/m²)
8.51
8.49
8.43
8.43
8.39
8.32
8.32

SOC
29.44
28.39
28.48
27.98
28.07
28.51
27.81

(nm/cm/MPa)

Maximum CT
340
189
200
192
184
178
220

(annealed; MPa)

Time for
72
20
20
20
18
64
28

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
218

D 430° C. (um²/hr)

1206
1356
1275
1465
292
1103

D430*CT
74120
227934
271200
244800
269560
51976
242660

(MPa · μm²/hour)

TABLE 2C

Property
15
16
17
18
19
20
21

Avg. CTE (10⁻⁷/C.)
56.4
55.4
56.9
54.6

60.8
55.7

(20-300° C.)

Strain (° C.)
645
650
645
682
603
662
671

Anneal (° C.)
690
696
689
727
648
707
717

Softening (° C.)
901

881

909

Density (g/cm³)
2.453
2.573
2.638
2.582
2.397
2.513
2.611

Liquidus
1395
1315
1245
1315
1345
1350
1295

temperature (° C.)

Liquidus viscosity
0.7
0.9
1.6
1.3
0.7
0.9
1.8

(kP)

K_1C(MPa√m)
0.863
0.858
0.866
0.864
0.820
0.854
0.857

Poisson's Ratio
0.231
0.233
0.237
0.232
0.218
0.228
0.227

Shear Modulus
36.47
36.20
36.87
36.75
33.51
36.20
36.54

(GPa)

Young's Modulus
89.77
89.22
91.01
90.60
81.63
88.87
89.63

(GPa)

Specific Modulus
36.60
34.67
34.50
35.09
34.06
35.37
34.33

(GPa · cm³/g)

G_1C(J/m²)
8.30
8.25
8.24
8.24
8.24
8.21
8.19

SOC
27.55
27.85
27.37
27.61
29.46
27.55
27.43

(nm/cm/MPa)

Maximum CT
280
275
280
270
393
330
265

(annealed; MPa)

Time for
48
32
25
24
48
36
24

maximum CT

(annealed, h)

Maximum CT

262

270

(fictivated; MPa)

Time for

20

24

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
435
324

383
500
1078
383

D 430° C. (um²/hr)
1364
832
521
1000
1153
1952
938

D430*CT
381920
228800
145880
270000
453129
644160
248570

(MPa · μm²/hour)

TABLE 2D

Property
22
23
24
25
26
27
28

Avg. CTE (10⁻⁷/C.)
56.5
46.4

57.1
52.9
61.2
50

(20-300° C.)

Strain (° C.)
679
717
656
650
660
644
693

Anneal (° C.)
724
762
699
694
705
688
738

Softening (° C.)

884

901
925

Density (g/cm³)
2.604
2.742

2.432
2.633
2.437
2.646

Liquidus
1365
1305
>1300
1385
1290
1355
1325

temperature (° C.)

Liquidus viscosity
0.5
1.6

0.7
1.2
1.1
1.1

(kP)

K_1C(MPa√m)
0.868
0.881
0.875
0.841
0.862
0.843
0.865

Poisson's Ratio
0.231
0.233
0.207
0.223
0.246
0.223
0.229

Shear Modulus
37.37
38.61
38.89
35.58
36.75
35.85
37.58

(GPa)

Young's Modulus
92.05
95.15
93.91
87.08
91.63
87.70
92.39

(GPa)

Specific Modulus
35.35
34.70

35.81
34.80
35.99
34.92

(GPa · cm³/g)

G_1C(J/m²)
8.19
8.16
8.15
8.12
8.11
8.10
8.10

SOC
27.05
26.79
34.14
27.55
26.71
27.68
27.09

(nm/cm/MPa)

Maximum CT
275
250
382
314
320
330
342

(annealed; MPa)

Time for
72
96.5
24
20
48
36
56

maximum CT

(annealed, h)

Maximum CT

280

(fictivated; MPa)

Time for

24

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
378
100
900
587

994
205

D 430° C. (um²/hr)
832
241
1725
1365
597
1855
546

D430*CT
228800
60250
658950
428610
191040
612150
186732

(MPa · μm²/hour)

TABLE 2E

Property
29
30
31
32
33
34
35

Avg. CTE (10⁻⁷/C.)
59.7
48.7
56.3
55.9
54.4
55.1
61

(20-300° C.)

Strain (° C.)
503
704
665
678
672
654
670

Anneal (° C.)
544
748
710
722
718
699
714

Softening (° C.)
740

906

Density (g/cm³)
2.354
2.678
2.64
2.65
2.425
2.557
2.558

Liquidus
1285
1305
1315
1275
1445
1300
1350

temperature (° C.)

Liquidus viscosity

1.6
1.2
1.8
0.4
2.0
0.8

(kP)

K_1C(MPa√m)
0.797
0.868
0.846
0.863
0.834
0.851
0.851

Poisson's Ratio
0.212
0.232
0.224
0.234
0.222
0.226
0.231

Shear Modulus
32.41
37.85
36.20
37.44
35.37
36.82
36.68

(GPa)

Young's Modulus
78.53
93.29
88.67
92.46
86.53
90.25
90.32

(GPa)

Specific Modulus
33.36
34.83
33.59
34.89
35.68
35.30
35.31

(GPa · cm³/g)

G_1C(J/m²)
8.09
8.08
8.07
8.06
8.04
8.02
8.02

SOC
30.25
27.02
27.2
27.02
28.01
27.35
27.2

(nm/cm/MPa)

Maximum CT
242
312
275
294
390
283
300

(annealed; MPa)

Time for
48
72
24
21.5
32
34
56

maximum CT

(annealed, h)

Maximum CT

266

261

(fictivated; MPa)

Time for

21

30

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
340
160
372

760

452

D 430° C. (um²/hr)

410
870
505
1885
834
1358

D430*CT
82280
127920
239250
148470
735150
236022
407400

(MPa · μm²/hour)

TABLE 2F

Property
36
37
38
39
40
41
42

Avg. CTE (10⁻⁷/C.)
58.4
51.2

65.9
59.6
50.8

(20-300° C.)

Strain (° C.)
612
695
625
655
612
690
652

Anneal (° C.)
660
742
668
701
661
735
696

Softening (° C.)
882
941

880

884

Density (g/cm³)
2.379
2.586
2.448
2.421
2.374
2.614

Liquidus
1325
1325
1355
1335
1365
1325
1285

temperature (° C.)

Liquidus viscosity
1.9
1.9
0.6
1.7
1.5
1.2

(kP)

K_1C(MPa√m)
0.799
0.848
0.843
0.827
0.801
0.854
0.854

Poisson's Ratio
0.218
0.226
0.224
0.218
0.219
0.234
0.202

Shear Modulus
32.68
36.61
36.27
35.09
33.03
37.09
38.13

(GPa)

Young's Modulus
79.63
89.77
88.74
85.49
80.46
91.49
91.56

(GPa)

Specific Modulus
33.47
34.71
36.25
35.31
33.89
35.00

(GPa · cm³/g)

G_1C(J/m²)
8.02
8.01
8.01
8.00
7.97
7.97
7.97

SOC
29.91
27.71
27
27.99
29.78
27.16
33.32

(nm/cm/MPa)

Maximum CT
330
316
470
374
340
370
380

(annealed; MPa)

Time for
24
40
64
16
16
48
20

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
1005
343
340
1121
1478
250
1135

D 430° C. (um²/hr)
2318
916
810
2576
2505
690
2195

D430*CT
764940
289456
380700
963424
851700
255300
834100

(MPa · μm²/hour)

TABLE 2G

Property
43
44
45
46
47
48
49

Avg. CTE (10⁻⁷/C.)
61.1
54.6
59.9
62.7

53

(20-300° C.)

Strain (° C.)
639
676
541
626
667
661
671

Anneal (° C.)
688
720
587
667
713
708
717

Softening (° C.)

919

Density (g/cm³)
2.393
2.548
2.353
2.463
2.862
2.42
2.42

Liquidus
1330
1355
1305
1345
>1290
1375
1410

temperature (° C.)

Liquidus viscosity
3.4
0.8

0.4

1.5
0.7

(kP)

K_1C(MPa√m)
0.804
0.842
0.781
0.843
0.829
0.825
0.823

Poisson's Ratio
0.208
0.230
0.214
0.231
0.189
0.222
0.219

Shear Modulus
33.58
36.27
31.72
36.61
36.61
35.30
35.23

(GPa)

Young's Modulus
81.22
89.29
76.95
90.05
87.08
86.25
85.84

(GPa)

Specific Modulus
33.94
35.04
32.70
36.56
30.43
35.64
35.47

(GPa · cm³/g)

G_1C(J/m²)
7.96
7.94
7.93
7.89
7.89
7.89
7.89

SOC
28.81
27.51
30.88
26.4
33.64
28.3
28.17

(nm/cm/MPa)

Maximum CT
250
405
305
450
275
315
380

(annealed; MPa)

Time for
11
32
48
72
16
4
30

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
1768
360
531
261
1520
1020
830

D 430° C. (um²/hr)
3764
1045

747
3306
2306
2134

D430*CT
941000
423225
161955
336150
909150
726390
810920

(MPa · μm²/hour)

TABLE 2H

Property
50
51
52
53
54
55
56

Avg. CTE (10⁻⁷/C.)

52.8
61.2
59.5
54
56.8
61

(20-300° C.)

Strain (° C.)
649
637
537
583
686
660
665

Anneal (° C.)
693
683
582
631
732
705
709

Softening (° C.)
885

794
840
927

906

Density (g/cm³)

2.623
2.353
2.365
2.615
2.667
2.432

Liquidus
>1310
1245
1290
1315
1320
1315
1420

temperature (° C.)

Liquidus viscosity

1.5
1.3
1.8
1.5
1.2
0.4

(kP)

K_1C(MPa√m)
0.842
0.842
0.778
0.788
0.846
0.833
0.826

Poisson's Ratio
0.203
0.242
0.221
0.219
0.230
0.230
0.228

Shear Modulus
37.37
36.27
31.58
32.41
37.09
35.92
35.44

(GPa)

Young's Modulus
89.98
90.11
77.01
79.01
91.15
88.39
87.08

(GPa)

Specific Modulus

34.36
32.73
33.41
34.86
33.14
35.81

(GPa · cm³/g)

G_1C(J/m²)
7.88
7.87
7.86
7.86
7.85
7.85
7.83

SOC
32.56
27.89
30.92
30.44
27.31
27.15
27.33

(nm/cm/MPa)

Maximum CT
375
310
335
360
250
272
485

(annealed; MPa)

Time for
20
56
40
32
24
32
32

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
1125

478
883
353
343
580

D 430° C. (um²/hr)
2235
493
1270
1966
930
833
1410

D430*CT
838125
152830
425450
707760
232500
226576
683850

(MPa · μm²/hour)

TABLE 2I

Property
57
58
59
60
61
62
63

Avg. CTE (10⁻⁷/C.)
52.2
58.8
54.7
64.6
60.7
57.9
57.5

(20-300° C.)

Strain (° C.)
686
491
672
653
559
663
664

Anneal (° C.)
730
529
717
701
604
708
710

Softening (° C.)

817

927

Density (g/cm³)
2.643
2.353
2.419
2.415
2.359
2.482
2.416

Liquidus
1320
1210
1390
1325
1285
1375
1390

temperature (° C.)

Liquidus viscosity
1.2
1.8
0.9
3.0

0.7
1.0

(kP)

K_1C(MPa√m)
0.849
0.791
0.820
0.815
0.779
0.826
0.816

Poisson's Ratio
0.231
0.216
0.220
0.215
0.225
0.232
0.216

Shear Modulus
37.37
32.89
35.23
34.96
31.65
35.44
35.03

(GPa)

Young's Modulus
92.05
79.91
85.91
84.87
77.57
87.22
85.15

(GPa)

Specific Modulus
34.83
33.96
35.51
35.14
32.88
35.14
35.24

(GPa · cm³/g)

G_1C(J/m²)
7.83
7.83
7.83
7.83
7.82
7.82
7.82

SOC
26.14
30.11
28.03
28.44
30.86
27.67
28.06

(nm/cm/MPa)

Maximum CT
330
214
390
295
340
448
430

(annealed; MPa)

Time for
48
50
32
13
48
20
18

maximum CT

(annealed, h)

Maximum CT

384

(fictivated; MPa)

Time for

16

maximum CT

(fictivated, h)

D 390° C. (um²/hr)

282
930
1513
556
555

D 430° C. (um²/hr)
697
740
2400
3350

1463
2084

D430*CT
230010
158360
936000
988250
189040
655424
896120

(MPa · μm²/hour)

TABLE 2J

Property
64
65
66
67
68
69
70

Avg. CTE (10⁻⁷/C.)
61.3
66.8

55.3
65.6

50.3

(20-300° C.)

Strain (° C.)
616
653
660
650
658
648
708

Anneal (° C.)
664
698
703
695
699
695
753

Softening (° C.)

911
891
897
887

940

Density (g/cm³)
2.395
2.42

2.557
2.446
2.404
2.737

Liquidus
1330
1345
>1320
1285
1445
1340
1340

temperature (° C.)

Liquidus viscosity
2.2
1.6

2.0
0.2
1.8
0.8

(kP)

K_1C(MPa√m)
0.802
0.818
0.837
0.843
0.829
0.801
0.859

Poisson's Ratio
0.214
0.219
0.208
0.232
0.228
0.213
0.235

Shear Modulus
33.85
35.16
37.16
36.96
35.85
33.92
38.33

(GPa)

Young's Modulus
82.25
85.70
89.77
91.08
88.11
82.32
94.73

(GPa)

Specific Modulus
34.34
35.41

35.62
36.02
34.24
34.61

(GPa · cm³/g)

G_1C(J/m²)
7.82
7.81
7.80
7.80
7.80
7.79
7.79

SOC
29.33
27.86
32.58
27.25
26.78
28.34
26.69

(nm/cm/MPa)

Maximum CT
290
355
400
290
530
370
290

(annealed; MPa)

Time for
18
16
24
18
40
24
88

maximum CT

(annealed, h)

Maximum CT

31

279

(fictivated; MPa)

Time for

14

17

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
1170
1300
1130

509
1025
134

D 430° C. (um²/hr)
2601
2874
2305
751
1350
2290
346

D430*CT
754290
1020270
922000
217790
715500
847300
100340

(MPa · μm²/hour)

TABLE 2K

Property
71
72
73
74
75
76
77

Avg. CTE (10⁻⁷/C.)
55.4
61.7

52
54.2
61.1
58.7

(20-300° C.)

Strain (° C.)
669
665
664
693
650
654
669

Anneal (° C.)
718
712
708
739
697
701
717

Softening (° C.)
943

932

920

Density (g/cm³)
2.404
2.418
2.992
2.599
2.397
2.425
2.397

Liquidus
1380
1355
>1320
1330
1395
1325
1405

temperature (° C.)

Liquidus viscosity
1.8
2.1
<1.3
1.4
1.6
2.8
1.2

(kP)

K_1C(MPa√m)
0.812
0.816
0.836
0.838
0.806
0.813
0.804

Poisson's Ratio
0.216
0.221
0.210
0.229
0.212
0.217
0.214

Shear Modulus
34.82
35.03
37.16
36.82
34.61
35.09
34.40

(GPa)

Young's Modulus
84.67
85.56
89.98
90.53
83.84
85.36
83.50

(GPa)

Specific Modulus
35.22
35.39
30.07
34.83
34.98
35.20
34.83

(GPa · cm³/g)

G_1C(J/m²)
7.79
7.78
7.77
7.76
7.75
7.74
7.74

SOC
28.54
28.34
33.61
27.41
28.67
28.13
28.73

(nm/cm/MPa)

Maximum CT
368
307
350
335
335
275
375

(annealed; MPa)

Time for
14
10
20
40
24
8
16

maximum CT

(annealed, h)

Maximum CT
317
281

(fictivated; MPa)

Time for
10
8.5

maximum CT

(fictivated, h)

D 390° C. (um²/hr)

1080
1255
317
1010
1048
1375

D 430° C. (um²/hr)
2488

2622
818
2405
2575
2343

D430*CT
915584
331560
917700
274030
805675
708125
878625

(MPa · μm²/hour)

TABLE 2L

Property
78
79
80
81
82
83
84

Avg. CTE (10⁻⁷/C.)
68.2
58.6
61.9
53.5
58
59.6
55.6

(20-300° C.)

Strain (° C.)
647
667
656
661
670
658
676

Anneal (° C.)
688
713
697
704
715
702
721

Softening (° C.)
897
930

888

Density (g/cm³)
2.436
2.415
2.529
3.272
2.423
2.465
2.651

Liquidus
1375
1375
1370
1315
1405
1370
1285

temperature (° C.)

Liquidus viscosity
0.3
1.3
0.5
0.7
0.6
0.9
1.5

(kP)

K_1C(MPa√m)
0.823
0.813
0.824
0.858
0.816
0.814
0.847

Poisson's Ratio
0.231
0.220
0.228
0.208
0.224
0.222
0.241

Shear Modulus
35.58
35.03
35.78
39.51
35.23
35.09
37.44

(GPa)

Young's Modulus
87.56
85.49
87.84
95.35
86.25
85.84
92.94

(GPa)

Specific Modulus
35.95
35.40
34.73
29.14
35.60
34.82
35.06

(GPa · cm³/g)

G_1C(J/m²)
7.74
7.73
7.73
7.72
7.72
7.72
7.72

SOC
26.84
28.36
26.55
34.53
27.92
27.51
26.88

(nm/cm/MPa)

Maximum CT
525
430
423
390
403
440
290

(annealed; MPa)

Time for
36
32
72
27
32
48
39

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
590
887
240
900
844
564

D 430° C. (um²/hr)
1320

654

2167
1510
690

D430*CT
693000
381410
276642
351000
873301
664400
200100

(MPa · μm²/hour)

TABLE 2M

Property
85
86
87
88
89
90
91

Avg. CTE (10⁻⁷/C.)
60.6
73.1
62.7
57.4
65.1

52.4

(20-300° C.)

Strain (° C.)
657
629
662
671
655
663
673

Anneal (° C.)
703
668
706
717
698
709
717

Softening (° C.)
923
841

869
907

Density (g/cm³)
2.434
2.453
2.415
2.406
2.423
2.929
2.677

Liquidus
1315
1435
1405
1385
1390
>1265
1345

temperature (° C.)

Liquidus viscosity
3.3
0.1
0.6
1.3
0.5

0.4

(kP)

K_1C(MPa√m)
0.816
0.830
0.807
0.805
0.811
0.828
0.858

Poisson's Ratio
0.226
0.230
0.215
0.214
0.219
0.203
0.245

Shear Modulus
35.23
36.47
34.89
34.75
35.09
37.09
38.54

(GPa)

Young's Modulus
86.46
89.63
84.74
84.32
85.63
89.29
95.91

(GPa)

Specific Modulus
35.52
36.54
35.09
35.05
35.34
30.48
35.83

(GPa · cm³/g)

G_1C(J/m²)
7.70
7.69
7.69
7.69
7.68
7.68
7.68

SOC
27.99
25.81
27.82
28.47
28
33.59
27.13

(nm/cm/MPa)

Maximum CT
271
525
475
395
460
305
325

(annealed; MPa)

Time for
10
26
11
24
26
16
72

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
875
388
935
1212
750
1390

D 430° C. (um²/hr)
2073
820
2575
2325
1800
3110
295

D430*CT
561783
430500
1223125
918375
828000
948550
95875

(MPa · μm²/hour)

TABLE 2N

Property
92
93
94
95
96
97
98

Avg. CTE (10⁻⁷/C.)
57.3
55.9
67.2
56.2

55.9

(20-300° C.)

Strain (° C.)
642
653
631
624
623
659
653

Anneal (° C.)
684
697
678
666
671
707
699

Softening (° C.)

872

Density (g/cm³)
2.464
2.838
2.418
2.52
2.918
2.426
2.404

Liquidus
1425
1340
1320
>1445
1230
>1340
1345

temperature (° C.)

Liquidus viscosity
0.2
1.0
2.7
<.17
4.3

1.8

(kP)

K_1C(MPa√m)
0.832
0.822
0.803
0.828
0.820
0.808
0.794

Poisson's Ratio
0.230
0.211
0.212
0.233
0.211
0.219
0.216

Shear Modulus
36.75
36.47
34.75
36.40
36.40
35.09
34.06

(GPa)

Young's Modulus
90.32
88.25
84.25
89.84
88.11
85.56
82.87

(GPa)

Specific Modulus
36.66
31.10
34.84
35.65
30.20
35.27
34.47

(GPa · cm³/g)

G_1C(J/m²)
7.66
7.66
7.65
7.63
7.63
7.63
7.61

SOC
26.78
32
28.2
27.75
34.2
28.48
28.38

(nm/cm/MPa)

Maximum CT
431
405
285
433
310
234
368

(annealed; MPa)

Time for
88
24
16
72
24
4
24

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
264
1066
1209
280
1090
1226
1100

D 430° C. (um²/hr)
662

3112
740
2200
2735
2423

D430*CT
285322
431730
886920
320420
682000
639990
891664

(MPa · μm²/hour)

TABLE 2O

Property
99
100
101
102
103
104
105

Avg. CTE (10⁻⁷/C.)
53.4
64.5
56.5
58.7
71
47.1
62.7

(20-300° C.)

Strain (° C.)
650
645
637
660
640
687
636

Anneal (° C.)
694
690
682
704
684
738
686

Softening (° C.)
883

995

Density (g/cm³)
3.266
2.4
2.46
2.436
2.441
2.377
2.385

Liquidus
1300
1380
1365
1370
1370
1370
1330

temperature (° C.)

Liquidus viscosity
0.8
1.0
0.9
0.9
0.6
7.1
4.1

(kP)

K_1C(MPa√m)
0.851
0.796
0.812
0.809
0.811
0.790
0.781

Poisson's Ratio
0.212
0.217
0.226
0.221
0.227
0.203
0.209

Shear Modulus
39.30
34.27
35.44
35.37
35.44
34.40
33.44

(GPa)

Young's Modulus
95.22
83.43
86.94
86.32
87.01
82.74
80.88

(GPa)

Specific Modulus
29.15
34.76
35.34
35.44
35.65
34.81
33.91

(GPa · cm³/g)

G_1C(J/m²)
7.61
7.59
7.58
7.58
7.56
7.54
7.54

SOC
34.82
28.16
27.99
27.59
27.37
29.95
29.15

(nm/cm/MPa)

Maximum CT
372
400
442
442
340
240
240

(annealed; MPa)

Time for

20.4
48
40
14
16
10

maximum CT

(annealed, h)

Maximum CT
315

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
945
1218
595
600
997
1260
1947

D 430° C. (um²/hr)

2410
1675
1460
2363
2888
4300

D430*CT
351540
964000
740350
645320
803420
693120
1032000

(MPa · μm²/hour)

TABLE 2P

Property
106
107
108
109
110
111
112

Avg. CTE (10⁻⁷/C.)
67.6

57.4
60.5
68.1
57
55.3

(20-300° C.)

Strain (° C.)
621
657
604
665
586
663
662

Anneal (° C.)
664
701
652
713
627
710
711

Softening (° C.)

894
868

Density (g/cm³)
2.447
2.993
2.383
2.404
2.452
2.456
2.393

Liquidus
1365
1285
1270
1350
>1375
>1445
1350

temperature (° C.)

Liquidus viscosity
0.3

2.9
2.9
<0.23
<.45
2.4

(kP)

K_1C(MPa√m)
0.815
0.828
0.771
0.794
0.816
0.803
0.785

Poisson's Ratio
0.223
0.211
0.222
0.213
0.220
0.218
0.217

Shear Modulus
36.06
37.58
32.27
34.54
36.27
35.23
33.72

(GPa)

Young's Modulus
88.11
91.01
78.94
83.77
88.53
85.77
82.05

(GPa)

Specific Modulus
36.01
30.41
33.13
34.85
36.10
34.92
34.29

(GPa · cm³/g)

G_1C(J/m²)
7.54
7.53
7.53
7.53
7.52
7.52
7.51

SOC
26.53
33.61
29.62
28.5
26.19
28.94
28.89

(nm/cm/MPa)

Maximum CT
536
335
320
311
530
401
333

(annealed; MPa)

Time for
48
20
24
16
64
24
16

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
404
1210
920
1480
280
840
1240

D 430° C. (um²/hr)
1110
2700
1910
3214
733
2011
3340

D430*CT
594960
904500
611200
999554
388490
806411
1112220

(MPa · μm²/hour)

TABLE 2Q

Property
113
114
115
116
117
118
119

Avg. CTE (10⁻⁷/C.)
75.7
64.9
55.6
62.6
58.6
62.1
47.4

(20-300° C.)

Strain (° C.)
614
647
663
616
586
631
674

Anneal (° C.)
652
693
714
666
633
675
728

Softening (° C.)

905
960

855
877

Density (g/cm³)
2.446
2.433
2.362
2.382
2.371
2.411
2.336

Liquidus
1375
1325
1410
1290
1290
1365
1365

temperature (° C.)

Liquidus viscosity
0.1
1.9
3.3
5.9
2.1
0.6
14.4

(kP)

K_1C(MPa√m)
0.815
0.805
0.775
0.769
0.762
0.779
0.764

Poisson's Ratio
0.224
0.223
0.196
0.214
0.222
0.220
0.196

Shear Modulus
36.13
35.30
33.51
32.68
31.92
33.58
32.96

(GPa)

Young's Modulus
88.46
86.39
80.19
79.29
77.98
81.91
78.88

(GPa)

Specific Modulus
36.17
35.51
33.95
33.29
32.89
33.97
33.77

(GPa · cm³/g)

G_1C(J/m²)
7.51
7.50
7.49
7.46
7.45
7.41
7.40

SOC
25.54
27.75
29.86
29.2
30.33
27.29
30.64

(nm/cm/MPa)

Maximum CT
550
300
272
225
335
430
200

(annealed; MPa)

Time for
36
10
11.25
12
24
24
10

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
358
954
2004
1791
737
800
2612

D 430° C. (um²/hr)
934
2567
4252
3964
2035
1955
4757

D430*CT
513700
770100
1156544
891900
681725
840650
951400

(MPa · μm²/hour)

TABLE 2R

Property
120
121
122
123
124
125
126

Avg. CTE (10⁻⁷/C.)
68.1
71
67.3
60.3
51
63.6
52.6

(20-300° C.)

Strain (° C.)
588
653
629
549
688
642
650

Anneal (° C.)
634
697
674
594
739
691
700

Softening (° C.)

891

990

Density (g/cm³)
2.428
2.43
2.437
2.385
2.369
2.385
2.369

Liquidus
1300
1375
1320
1335
1410
1335
1315

temperature (° C.)

Liquidus viscosity
2.4
0.3
1.9
1.2
4.3
3.5
5.3

(kP)

K_1C(MPa√m)
0.795
0.798
0.797
0.778
0.775
0.772
0.760

Poisson's Ratio
0.224
0.221
0.220
0.213
0.205
0.212
0.210

Shear Modulus
34.96
35.37
35.30
33.85
33.85
33.44
32.47

(GPa)

Young's Modulus
85.49
86.32
86.12
82.12
81.63
81.01
78.60

(GPa)

Specific Modulus
35.21
35.52
35.34
34.43
34.46
33.97
33.18

(GPa · cm³/g)

G_1C(J/m²)
7.39
7.38
7.38
7.37
7.36
7.36
7.35

SOC
27.68
26.71
27.56
29.11
29.84
29.19
29.52

(nm/cm/MPa)

Maximum CT
285
530
300
350
270
259
250

(annealed; MPa)

Time for
24
32
24
24
15
7.3
16

maximum CT

(annealed, h)

Maximum CT

226

(fictivated; MPa)

Time for

6

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
750
577
825
635
1637
1590
1636

D 430° C. (um²/hr)
2053
1385
2038
1315
3676

3917

D430*CT
585105
734050
611400
460250
992520
411810
979250

(MPa · μm²/hour)

TABLE 2S

Property
127
128
129
130
131
132
133

Avg. CTE (10⁻⁷/C.)
70.1

59.8
68.4
66.8
57.7
60.3

(20-300° C.)

Strain (° C.)
541
632
654
635
635
664
622

Anneal (° C.)
583
679
695
679
684
709
665

Softening (° C.)

Density (g/cm³)
2.437
2.392
2.472
2.416
2.407
2.416
2.449

Liquidus
1340
1350
1390
1400
1280
1325
1335

temperature (° C.)

Liquidus viscosity
0.4
1.4
0.4
0.4
5.8
2.2
0.7

(kP)

K_1C(MPa√m)
0.801
0.769
0.808
0.789
0.773
0.787
0.802

Poisson's Ratio
0.225
0.215
0.230
0.222
0.216
0.219
0.229

Shear Modulus
35.71
33.16
36.20
34.82
33.78
35.03
36.20

(GPa)

Young's Modulus
87.43
80.60
89.15
85.08
82.19
85.36
88.94

(GPa)

Specific Modulus
35.87
33.70
36.06
35.22
34.14
35.33
36.32

(GPa · cm³/g)

G_1C(J/m²)
7.34
7.34
7.32
7.32
7.27
7.26
7.23

SOC
26.44
28.62
26.73
27.51
28.78
28.28
27.13

(nm/cm/MPa)

Maximum CT
450
325
410
450
216
400
400

(annealed; MPa)

Time for
64
4
37
20
12

maximum CT

(annealed, h)

Maximum CT

350
360

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
248
1150
253
833
1660
945
400

D 430° C. (um²/hr)
676
2515
652

3840

D430*CT
304200
817375
267320
374850
829440
378000
160000

(MPa · μm²/hour)

TABLE 2T

Property
134
135
136
137
138
139
140

Avg. CTE (10⁻⁷/C.)
53.8
60.2
59.7
59.3
54.4
74.7
63.5

(20-300° C.)

Strain (° C.)
681
660
668
649
659
638
603

Anneal (° C.)
730
707
715
698
709
683
652

Softening (° C.)
970

960

Density (g/cm³)
2.379
2.392
2.388
2.387
2.366
2.445
2.371

Liquidus
1400
1390
1405
1370
1365
1345
1290

temperature (° C.)

Liquidus viscosity
2.9
1.4
1.6
1.8
4.4
1.1
6.7

(kP)

K_1C(MPa√m)
0.772
0.769
0.770
0.764
0.757
0.780
0.746

Poisson's Ratio
0.210
0.208
0.207
0.208
0.208
0.216
0.200

Shear Modulus
34.06
33.92
34.06
33.51
32.96
34.89
32.41

(GPa)

Young's Modulus
82.53
81.91
82.19
80.94
79.70
84.87
77.77

(GPa)

Specific Modulus
34.69
34.24
34.42
33.91
33.69
34.71
32.80

(GPa · cm³/g)

G_1C(J/m²)
7.22
7.22
7.21
7.21
7.19
7.17
7.16

SOC
29.58
28.88
29.18
29.06
29.8
27.7
29.4

(nm/cm/MPa)

Maximum CT
250
365
375
340
260
270
225

(annealed; MPa)

Time for
15
16
16
16
15
13
10

maximum CT

(annealed, h)

Maximum CT

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
950
1403
1530
1466
1723
1175
2025

D 430° C. (um²/hr)
3480

2800
2965

2675
4254

D430*CT
870000
512095
1050000
1008100
447980
722250
957150

(MPa · μm²/hour)

TABLE 2U

Property
141
142
143
144
145

Avg. CTE (10⁻⁷/C.)
59.5
67.9
52.1
60.9
88.6

(20-300° C.)

Strain (° C.)
648
647
667
643
650

Anneal (° C.)
698
694
719
692
694

Softening (° C.)

972

883

Density (g/cm³)
2.381
2.426
2.356
2.38
3.266

Liquidus
1330
1325
1360
1390

temperature (° C.)

Liquidus viscosity
5.4
2.3
7.5
1.7

(kP)

K_1C(MPa√m)
0.760
0.781
0.745
0.761
0.851

Poisson's Ratio
0.212
0.223
0.195
0.211
0.212

Shear Modulus
33.37
35.09
32.75
33.85
39.30

(GPa)

Young's Modulus
80.81
85.91
78.26
81.98
95.22

(GPa)

Specific Modulus
33.94
35.41
33.22
34.44
29.15

(GPa · cm³/g)

G_1C(J/m²)
7.15
7.10
7.09
7.06
7.61

SOC
29.16
28.15
30.09
28.9
34.82

(nm/cm/MPa)

Maximum CT
235
290
230
348
372

(annealed; MPa)

Time for
12
14
15

maximum CT

(annealed, h)

Maximum CT

277
315

(fictivated; MPa)

Time for

maximum CT

(fictivated, h)

D 390° C. (um²/hr)
1840
1437
1925
1380

D 430° C. (um²/hr)
4182
3165
4300

D430 * CT
982770
917850
989000
480240

(MPa · μm²/hour)

The glass-based articles prepared as above were investigated for the ability to survive repeated drops on damaging surfaces. Glasses were double melted for homogeneity and then cut into phone-size glass-based substrates and polished to dimensions of 110 mm×56 mm×0.8 mm. The glass-based substrates were ion exchanged for various times to find the maximum CT, providing glass-based articles. The glass-based articles were then mounted in a drop device (e.g., identical mobile phone devices, such as an IPHONE® 3GS, or a puck simulating the size and weight of a mobile phone device, wherein the puck had a weight of 135 g) and dropped onto 180 grit sandpaper from incremental heights starting at 20 cm. If a glass-based article survived the drop from one height (e.g., 20 cm), the glass-based article was dropped again from a 10 cm greater height (e.g., 30 cm, 40 cm, 50 cm, etc.) up to a maximum height of 220 cm. A glass-based article is said to have survived if there are no cracks visible to the naked eye. Survivors then went on to be dropped on 30 grit sandpaper. FIG. 2 compares the drop performance of a glass-based article made from composition 145 versus previous technologies. CE1 is a glass article made from a glass composition comprising 57.43 mol. % SiO₂, 16.1 mol. % Al₂O₃, 17.05 mol. % Na₂O, 2.81 mol. % MgO, 0.003 mol. % TiO₂, 0.07 mol. % SnO₂, and 6.54 mol. % P₂O₅. CE2 is a glass article made from a glass composition comprising 63.60 mol. % SiO₂, 15.67 mol. % Al₂O₃, 10.81 mol. % Na₂O, 6.24 mol. % Li₂O, 1.16 mol. % ZnO, 0.04 mol. % SnO₂, and 2.48 mol. % P₂O₅. CE3 is a glass article made from a glass composition comprising 70.94 mol. % SiO₂, 1.86 mol. % B₂O₃, 12.83 mol. % Al₂O₃, 2.36 mol. % Na₂O, 8.22 mol. % Li₂O, 2.87 mol. % MgO, 0.83 mol. % ZnO, 0.022 mol. % Fe₂O₃, and 0.06 mol. % SnO₂. CE4 is a glass article made from a glass composition comprising 69.26 mol. % SiO₂, 1.83 mol. % B₂O₃, 12.58 mol. % Al₂O₃, 0.41 mol. % Na₂O, 7.69 mol. % Li₂O, 2.85 mol. % MgO, 1.73 mol. % ZnO, 3.52 mol. % TiO₂, and 0.13 mol. % SnO₂. While CE1 fails at an average drop height of 35 cm, other glasses, CE2, CE3, and CE4, can increase the average drop height to failure to 66, 115 cm, and 149 cm, respectively. By increasing the CT, modulus and fracture toughness, the glass-based article made from composition 145 showed no failures and maxed out the test at 220 cm drop height.

Without intending to be bound by any particular theory, it is believed that to maximize CT, a large number of alkali ions should be available for exchange. Because the alkalis associated with Al₂O₃in the glass structure are the most mobile, the glass should have a high alkali aluminate (R₂O Al₂O₃) content of 8 mol. % or greater (where R is Li or Na) for sufficient stress and ion exchange rates. FIG. 3 shows the maximum central tension CT for near charge balanced lithium alumino silicates (shown as diamonds). To achieve greater than 175 MPa CT, the glass should have at least 10 mol. % Li₂O.Al₂O₃for simple ternary glasses.

However by increasing the elastic modulus of the glass, the amount of stress per ion can be increased and lower amounts of Li₂O.Al₂O₃can be used to achieve the same maximum CT. Small cations with high field strength, such as MgO and Y₂O₃, may be used for this purpose. The data points shown as squares in FIG. 3 represent data using Y₂O₃−Li₂O₃—Al₂O₃—SiO₂based glass articles. From FIG. 3, it is possible to see that higher maximum CT values may be obtained with Y₂O₃-containing lithium alumino silicates. In fact, only about 5 mol. % of Li₂O (or 5 mol. % Li₂O.Al₂O₃) is needed for attaining a maximum CT of 1751 MPa. Y₂O₃may also increase K_1Cand G_1C, as illustrated in FIG. 4. It is also believed that Y₂O₃may also help improve the liquidus viscosity until one of yttrium disilicate or Keivyite becomes the liquidus phase. Ta₂O₅has similar effects (not shown).

As shown in FIG. 5, a glass-based article made from composition 17 has a 92% survival rate after thirty 1 m drops onto 30 grit sandpaper, while CE1 ion exchanged to a slightly higher CT (285 MPa for CE1 versus 280 MPa for the composition 17 article) only has a 15% survival rate. Without intending to bound to any particular theory, it is believed that the difference is due to the higher fracture toughness K_1C, and more specifically, the higher critical strain energy release rate G_1Cof the glass-based article made from composition 17. While CE1 only has a G_1Cof 6.82 J/m², the composition 17 article has a 20% higher G_1Cof 8.24 J/m². Similarly, a glass-based article made from composition 81 had a 60% survival rate, and glass-based articles made from composition 79 had about a 50% survival rate. Both of these glass-based articles had higher K_1C(and thus higher G_1C) than CE1.

FIG. 6 shows repeated drop to failure survival as a function of central tension for 0.8 mm thick specimens. Without intending to be bound to any particular theory, it is believed that although CT has a profound effect on survivability, the inventive glasses (represented as dots) have superior survival rates to CE1 (shown as the square at a CT of 285 MPa and 20% survival) because they have greater fracture toughness, elastic modulus, and critical strain energy release rates. That CE1 has a survivability that is significantly below the trend line at CT=285 MPa suggests that properties beyond just CT are involved in the survivability values obtained from the inventive compositions.

FIG. 7 shows the effect on K_1Cand Young's modulus of replacing Li₂O and Na₂O through ion exchange. As the amount of Na₂O is increased, the Young's modulus and fracture toughness decrease, and as a result, the high Na₂O content glass-based articles do not exhibit favorable drop performance.

FIG. 8 shows the stress profile for a 1 mm-thick glass-based article made from composition 62. It should be noted that the stress values above the local minima ranging from 0.85 mm to 1 mm and below the local minima ranging from 0.05 mm to 0.15 mm are measurement artifacts. The glass-based article was ion exchanged in a 100% NaNO₃bath at 430° C. for 16 hours. The maximum CT was 442.7 MPa, and the stored strain energy was 459.6 J/m². In contrast, the highest maximum CT attained in CE1 is 285 MPa, and this is only after four days of ion exchange. Without intending to be bound by any particular theory, it is believed that the high content of Li₂O.Al₂O₃enables the achievement of such high stresses while the higher mutual diffusivity of Na⁺for Li⁺ enables this to be achieved in hours as opposed to days. It is believed that the much higher mutual diffusivity of Na⁺for Li⁺ compared with the mutual diffusivity of K⁺for Na⁺is a contributing factor in this behaviour.

Referring back to Tables 2A-2U, the mutual diffusivity D increased with the temperature increase from 390° C. to 430° C., indicating that higher diffusivity may be achieved at higher ion exchange temperatures. However, stress relaxation occurs as the temperature increases. Accordingly, the high diffusivity could potentially be associated with lower CT. Therefore, the arithmetic product of the maximum CT and the diffusivity may provide an indication of merit for cost and performance.

It will be apparent to those skilled in the art that various modifications and variations can be made to the embodiments described herein without departing from the spirit and scope of the claimed subject matter. Thus it is intended that the specification cover the modifications and variations of the various embodiments described herein provided such modification and variations come within the scope of the appended claims and their equivalents.

HIGH FRACTURE TOUGHNESS GLASSES WITH HIGH CENTRAL TENSION

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