Glass with reduced non-viscous relaxation to achieve improved overall pitch variation

Abstract

The present disclosure describes a glass composition having reduced non-viscous relaxation and improved overall pitch variation, including SiO2, Al2O3, B2O3, MgO, CaO, SrO, BaO, TiO2, ZnO, Y2O3, La2O3, P2O5, and satisfying the following condition: # imgabs0 # wherein the symbol "*" represents a multiplication, Xi is the coefficient of the oxide component, the value Yi is the amount of oxide component in mol%. Glass manufactured from the glass composition of the present application has a very small dimensional change during a thermal cycle, and glass substrates manufactured from the glass composition of the present application have a very small consistent total pitch change from one glass substrate to the next glass substrate.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the priority benefit of U.S. Provisional Application Serial No. 63 / 583694 filed on September 19, 2023 under the Patent Law, the contents of which are the basis for this application and are incorporated herein by reference in their entirety. Technical Field

[0003] The present disclosure relates to glass compositions, and in particular, glass compositions that exhibit reduced overall pitch variation. Background Art

[0004] Display panel manufacturers rely on predictable glass properties to manage the manufacturing and assembly of glass components, such as backplanes and color filters. Glass should have minimal dimensional changes during thermal cycles such as temperature excursions (such as those experienced by glass during the thin film formation process). More importantly, glass substrates used for such manufacturing should have minimal consistent overall pitch variation from one glass substrate to the next.

[0005] In view of these factors, there exists a need for glass compositions that exhibit reduced inviscid relaxation combined with improved overall spacing change. Summary of the invention

[0006] In a first aspect, a glass is disclosed, comprising:

[0007] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0008] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0009] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0010] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0011] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0012] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0013] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0014] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0015] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0016] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0017] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0018] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0019] The glass meets the following conditions: where the symbol "*" represents multiplication, and

[0020] Intercept = -11.20751259,

[0021] The coefficient Xi of the component oxide is:

[0022] SiO2=-0.002926308,

[0023] Al2O3=-0.004673511,

[0024] B2O3=-0.001118634,

[0025] MgO=1.126496816,

[0026] CaO=1.615716878,

[0027] SrO = 3.063872526,

[0028] BaO=1.551023535,

[0029] TiO2=-0.004673511,

[0030] ZnO=0,

[0031] Y2O3=-0.001118634,

[0032] La2O3=-0.001118634,

[0033] P2O5 = -2.235863244; and

[0034] in,

[0035] SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%,

[0036] MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%,

[0037] TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

[0038] In a second aspect, a glass is disclosed, comprising:

[0039] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0040] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0041] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0042] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0043] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0044] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0045] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0046] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0047] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0048] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0049] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0050] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0051] The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -234.7571088, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0052] SiO2=2.232090497,

[0053] Al2O3=2.230475478,

[0054] B2O3=2.233717001,

[0055] MgO=3.368563490,

[0056] CaO=3.851331728,

[0057] SrO = 5.301366502,

[0058] BaO=3.788612774,

[0059] TiO2=2.230475478,

[0060] ZnO=2.23468972,

[0061] Y2O3=2.233717001,

[0062] La2O3=2.233717001,

[0063] P2O5=0; and

[0064] in,

[0065] SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%,

[0066] MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and

[0067] TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

[0068] In a third aspect, a glass is disclosed, comprising:

[0069] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0070] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0071] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0072] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0073] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0074] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0075] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0076] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0077] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0078] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0079] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0080] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0081] The glass meets the following conditions:

[0082] Where the symbol "*" indicates multiplication, the intercept = -237.7578217, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0083] SiO2=2.25149345,

[0084] Al2O3=2.250724382,

[0085] B2O3=2.252392713,

[0086] MgO=3.524128464,

[0087] CaO=3.890462587,

[0088] SrO = 5.366534992,

[0089] BaO=3.897785139,

[0090] TiO2=2.250724382,

[0091] ZnO=2.253175066,

[0092] Y2O3=2.252392713,

[0093] La2O3=2.252392713,

[0094] P2O5=0; and

[0095] in,

[0096] SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%,

[0097] MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and

[0098] TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

[0099] In a fourth aspect, a glass is disclosed, comprising:

[0100] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0101] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0102] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0103] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0104] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0105] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0106] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0107] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0108] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0109] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0110] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0111] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0112] The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -242.7132028, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0113] SiO2=2.260131924,

[0114] Al2O3=2.260271613,

[0115] B2O3=2.26056072,

[0116] MgO=3.878171611,

[0117] CaO=4.168656199,

[0118] SrO=5.552077225,

[0119] BaO=4.212721511,

[0120] TiO2=2.260271613,

[0121] ZnO=2.259907435,

[0122] Y2O3=2.26056072,

[0123] La2O3=2.26056072,

[0124] P2O5=0; and

[0125] in,

[0126] SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%,

[0127] MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and

[0128] TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

[0129] The foregoing general description and the following detailed description present embodiments that are intended to provide an overview or framework for understanding the nature and character of the embodiments disclosed herein. The accompanying drawings are included to provide a further understanding and are incorporated into and constitute a part of this specification. The drawings illustrate various embodiments of the present disclosure and together with the description explain its principles and operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] Figure 1 is a graph of temperature (vertical axis) versus time (horizontal axis) for a test procedure that can be used to observe fast relaxation in display glass. The times, temperatures, and slopes shown in this figure are not drawn to scale. The test procedure includes conditioning phases 10, 12, 14 and measurement phases 16, 18, 20;

[0131] Figure 2 is shown similar to Figure 1 Schematic diagram (not drawn to scale) of another embodiment of a test of a test procedure of wherein the vertical axis is the temperature of the heating cycles 26, 28, 30, 32 and the imaginary temperature of the curves 22 and 24, and the horizontal axis is time;

[0132] Figure 3 It is shown Figure 2 A schematic diagram (not drawn to scale) of a dimensional change resulting from a measurement phase of a test procedure of FIG. 1 , wherein the vertical axis is the dimensional change, for example in parts-per-million (ppm), and the horizontal axis is scaled in time;

[0133] Figure 4 is a graph giving an indication of the agreement between the genetic algorithm based predictions according to the best model and the measured data;

[0134] Figure 5 is a graph showing the accuracy of predictions using a genetic algorithm based model compared to measured data;

[0135] Figure 6 is another graph showing the accuracy of predicted results using a genetic algorithm based model compared to measured data;

[0136] Figure 7 is a graph of the convex hull of the glass composition according to the present disclosure, wherein the intercept is equal to or less than 16;

[0137] Figure 8 is a graph of the convex hull of the glass composition according to the present disclosure, wherein the intercept is equal to or less than 13;

[0138] Fig. 9 is a plot of the convex hull of the glass composition according to the present disclosure, wherein the intercept is equal to or less than 10;

[0139] Fig.10 is a plot of the convex hull of a glass composition according to the present disclosure, wherein the intercept is equal to or less than 8; and

[0140] Fig.11 yes Figures 7 to 10 Nested plot of the convex hull of . DETAILED DESCRIPTION

[0141] Reference will now be made in detail to embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numerals will be used to refer to the same or similar parts in all the accompanying drawings. However, the present disclosure may be embodied in many different forms and should not be considered to be limited to the embodiments described herein.

[0142] As used herein, the term "about" means that quantities, sizes, formulations, parameters and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller as necessary to reflect tolerances, conversion factors, rounding, measurement errors, etc. and other factors known to those skilled in the art.

[0143] As used herein, the term "about" means that quantities, sizes, formulations, parameters and other quantities and characteristics are not and do not need to be exact, but may be approximate and / or larger or smaller as needed to reflect tolerances, conversion factors, rounding, measurement errors, etc. and other factors known to those skilled in the art. When the term "about" is used to describe the endpoints of a value or range, the disclosure should be understood to include the specific values ​​or endpoints mentioned. Regardless of whether the endpoints of a numerical value or range in this specification are expressed as "about", the endpoints of the numerical value or range are intended to include two embodiments: one modified by "about" and one not modified by "about". It should be further understood that the endpoints of each range are significant relative to the other endpoints and independently of the other endpoints.

[0144] Directional terms (eg, up, down, right, left, front, back, top, bottom) that may be used herein refer only to the figures drawn and are not intended to imply absolute positions.

[0145] Unless otherwise expressly stated, it is not intended that any method set forth herein be construed as requiring that its steps be performed in a particular order, nor that any apparatus require a particular orientation. Thus, in the absence of a method claim actually reciting the order in which its steps are to be followed, or any apparatus claim actually reciting the order or orientation of individual components, or in the absence of another specific statement in the claim or specification that the steps are limited to a particular order, or in the absence of a specific order or orientation of apparatus components, no order or orientation is intended to be inferred in any respect. This applies to any possible non-explicit basis for interpretation, including matters of logic regarding arrangement of steps, operational flow, order of components, or orientation of components; clear meaning derived from grammatical organization or punctuation; and the number or type of embodiments described in the specification.

[0146] 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 dictates otherwise.

[0147] The words "exemplary," "example," or various forms thereof, are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as "exemplary" or "example" should not be construed as being preferred or advantageous over other aspects or designs. In addition, examples are provided solely for the purpose of clarity and understanding and are not intended to limit or restrict the disclosed subject matter or relevant portions of the present disclosure in any way. It is understood that a large number of additional or alternative examples of varying scopes could have been presented, but these examples have been omitted for the sake of brevity.

[0148] As used herein, the terms "include" and "comprising" and variations thereof should be interpreted as synonymous and open-ended unless otherwise indicated. A list of elements following the transitional phrase "include" or "comprising" is a non-exclusive list, and thus additional elements may be present in addition to the elements explicitly recited in the list.

[0149] As used herein, the terms "substantially," "substantially," and variations thereof are intended to indicate that the feature being described is equal to or approximately equal to a certain value or description. For example, a "substantially planar" surface is intended to mean a planar or approximately planar surface. Additionally, "substantially" is intended to mean that two values ​​are equal or approximately equal. In some embodiments, "substantially" may mean values ​​that are within about 10% of each other, such as within about 5% of each other, within about 2% of each other, within about 1% of each other, or within 0.5% of each other.

[0150] For the sake of brevity, a range of values ​​(including composition ranges or attribute (performance) ranges) or a series of ranges disclosed herein may be appended with the phrase "including all ranges and subranges therebetween", which should be interpreted as including integer or decimal subranges, as if explicitly presented. Thus, for example, a range between 6 and 8 (omitting the unit) implicitly includes a subrange between 6.4 and 8, or a subrange between 6 and 7.2, or a subrange between 6 and 7, etc. In addition, a series of ranges, such as "in the range from 6 to 11 or in the range from 6 to 8" implicitly includes a range from 7 to 10, or a subrange therebetween, such as 7.2 to 10.4, as if explicitly presented, as long as the range does not exceed the minimum or maximum endpoint of the range or series of ranges explicitly presented.

[0151] The symbol "*" when used in any formula herein means multiplication.

[0152] From a thermodynamic point of view, a glass is a nonequilibrium system that relaxes to a metastable supercooled liquid state. This relaxation typically involves continuous changes in volume, enthalpy, and other properties of the glass as it approaches the liquid state. While the presence of a thermodynamic driving force is a necessary condition for glass relaxation, it is not sufficient by itself, as the glass must also have sufficient thermal energy and / or time to achieve the relaxation dynamics. Assuming isobaric conditions, the dynamics of a glass depends on three factors: composition, temperature, and thermal history. The importance of thermal history cannot be overstated, as the dynamics of two glasses of the same composition and at the same temperature can differ by many orders of magnitude depending on the details of the thermal history.

[0153] When a glass melt is rapidly cooled from a high temperature, the motion of the atoms within the coolant slows as the temperature decreases and is eventually reduced to oscillations about fixed positions due to normal thermal focusing of the vibrational states. These positions are generally not the positions that the glass will adopt when it is required to be held at an intermediate temperature (e.g., a glass transition temperature or a strain or annealing point) for a longer period of time (from seconds to days). Therefore, when the rapidly quenched glass is reheated to the intermediate temperature, the thermally focused vibrational states allow the atoms to relax to positions that better meet their individual and collective bonding requirements. Since this is usually accompanied by a reduction in the physical size of the glass mass, thermal relaxation upon reheating is said to result in compaction of the glass.

[0154] The amount of compaction exhibited by any glass sample upon reheating will depend on the fictive temperature of the glass at the start of reheating, i.e., T. f (t0), and the change in the hypothetical temperature during the reheating process, i.e., T f (t). The change of the fictive temperature with time when reheating to temperature T can be described by the following equation:

[0155] (T f (t) – T) = (Tf (t0) – T) * exp [(-t / τ(T)) b ] (1)

[0156] Here, b is the "stretch constant" and τ(T) is the relaxation time of the glass at the heat treatment temperature.

[0157] The relaxation time of glass at a given temperature T can be approximated by the following formula:

[0158] τ(T)≈η(T) / G(2)

[0159] where η(T) is the shear viscosity of the glass at a given temperature and G is the shear modulus of the glass, which scales the viscosity to time space and is independent of temperature in a first approximation.

[0160] It can be seen from equations (1) and (2) that as the relaxation time increases (e.g., by increasing η(T)), the hypothetical temperature change of the glass over a set amount of time is significantly reduced, thereby reducing the compaction rate measured in a set thermal cycle.

[0161] Although the fictive temperature is often referred to as a single temperature for a given quench rate, this is merely a linguistic convenience since experimental evidence has clearly demonstrated the existence of a distribution of relaxation times in glasses of the type used as display substrates.

[0162] Glass sheets for incorporation into display substrates, especially glass sheets as glass substrates for thin film deposition, are first formed into glass ribbons from molten material, then cooled to form an elastic solid, and then cut into individual glass sheets. These glass sheets are sold to display manufacturers, who further process the glass sheets by depositing thin films in processes that involve exposing the glass sheets to high temperatures, such as in excess of 400°C. This exposure can cause dimensional changes in the glass compared to the as-manufactured state of the original glass sheet. In addition, the presence of one or more thin films and the resulting stresses can affect the behavior of the glass.

[0163] Total pitch variation (TPV) is a glass sheet property that customers of high precision display (HPD) glass are concerned about in their panel manufacturing process. TPV refers to the dimensional change from one glass sheet to another. For example, by way of a simple experiment, consider a glass sheet sample placed on a flat surface that includes a fiducial mark. A corresponding mark is made on the glass sample. The flat surface includes a stopper that is arranged to allow the glass sheet to be placed in the same position after the glass sheet is removed and then placed back on the flat surface. The glass sample is removed from the flat surface and subjected to a thermal drift sufficient to cause a dimensional change in the glass sheet sample. The glass sheet sample is then placed back on the flat surface and the stopper is used to position the glass sheet in the same position it was previously in. A second mark is made on the glass sheet that corresponds to the fiducial mark. The distance between the first mark on the glass sheet sample before the thermal drift and the second mark on the glass sheet sample after the thermal drift represents the pitch.

[0164] The thin film deposition process relies on precise registration between deposited layers. Display panel manufacturers want each glass sheet to be identical. Even very small registration variations (on the order of a few microns) can have a significant impact on the formation of the TFT (which includes thin film deposition, lithography, etching, and thermal treatment processes). However, it is clear from the previous discussion that the glass sheet will undergo dimensional changes due to the thermal history of the glass sheet. Therefore, it is at least desirable that the dimensional change (pitch) exhibited by the next glass sheet is the same as the dimensional change (pitch) experienced by the previous glass sheet. If the dimensional changes are consistent, the panel manufacturer can account for the dimensional changes. However, if the pitch experienced by one glass sheet is different from the pitch experienced by the second glass sheet, it becomes more difficult to accommodate this pitch variation. TPV, then, is the pitch variation exhibited in a population (or a sample thereof) of glass products (such as glass sheets).

[0165] When a display panel manufacturer uses glass in its process, it can measure four main components that act on the TPV: elastic deformation, stress relaxation, viscous relaxation (compaction), and non-viscous relaxation (which also contributes to compaction). Although both viscous relaxation and non-viscous relaxation contribute to the overall compaction part of the TPV, the difference between the two lies in the temperature regime at which compaction occurs. Non-viscous relaxation is considered to be driven by the glass chemistry and occurs in a temperature range far below the annealing point in HPD-class glasses, e.g., <450 °C. On the other hand, viscous relaxation occurs in a temperature range slightly below the annealing point up to about 450 °C. Note that these temperature ranges depend on the annealing point, so the ranges expressed above only apply to HPD-class glasses with an annealing point of about 800 °C and higher. Additionally, viscous relaxation is driven by the change in viscosity that occurs when the glass is heated and undergoes relaxation to the thermodynamically required volume. It is believed that in a higher temperature range, each glass undergoes both viscous relaxation and non-viscous relaxation simultaneously. However, in a lower temperature range, the glass viscosity is too high for any relaxation (compaction) related to viscosity change to occur within one to two hours during which the panel manufacturer processes the glass. However, non-viscous relaxation occurs very quickly, so the panel manufacturer often sees compaction occur at very low temperatures within a very short (30 minutes to 1 hour) processing time.

[0166] By considering the glass as consisting of two populations of relaxation substances, namely "fast relaxants" and "slow relaxants", the dimensional behavior of the glass when subjected to the thermal cycles used in display manufacturing can be reasonably approximated and controlled. Specifically, the method of controlling dimensional changes by fast relaxant - slow relaxant is applicable to a specific thermal cycle in which a glass plate undergoes at least first and second heating stages, the first heating stage being characterized by a maximum temperature T1 and a late cooling rate r1, and the second heating stage being characterized by a maximum temperature T2 and a late cooling rate r2, where:

[0167] T1 < T2 and r1 = r2; or (3)

[0168] T1 = T2 and r1 < r2; or (4)

[0169] T1 < T2 and r1 < r2. (5)

[0170] The main thermal cycle in the display manufacturing process is usually the second heating stage in this two-stage heating process. Therefore, the ability to control the dimensional change of the glass plate in this second heating stage by adjusting the relative amounts of fast and slow relaxants that make up the glass plate makes an important contribution to the display manufacturing process.

[0171] Generally speaking, the viscosity and temperature behavior of the glass (e.g., the annealing temperature of the glass (i.e., the glass viscosity is balanced at 10 13.18 Specifically, slow relaxants are relaxants whose behavior can be described to a first approximation by equation (4), while fast relaxants are those whose relaxation times are faster than predicted by equation (4).

[0172] In fact, the presence of slow and fast relaxers can cause the glass to exhibit dimensional changes when subjected to a two-phase temperature step. Specifically, the glass can experience expansion first, followed by contraction. This is especially the case in short thermal cycles, such as "rapid thermal annealing" or "RTA (rapid thermal anneal)" commonly used in display manufacturing, where fast relaxers can cause expansion in a short period of time instead of traditional compaction, thus playing a significant role in the net dimensional change of the glass.

[0173] The overall behavior can be controlled by selecting or adjusting the number and / or amount of fast relaxers in the glass. However, to do this requires being able to distinguish the effects of fast relaxers from those of slow relaxers. Figure 1 The testing procedure used to obtain this separation between slow and fast relaxer effects is shown.

[0174] from Figure 1 As can be seen from the figure, the test procedure consists of a conditioning phase ( Figure 3 10, 12, 14 of them; Figure 2 26) and the measurement phase ( Figure 1 16, 18, 20; Figure 2 28, 30, 32). The adjustment phase consists of three periods, among which:

[0175] (i) In the first period of the conditioning phase, the glass is heated from room temperature (e.g., 20° C.) to 656° C. (see Figure 1 10 in );

[0176] (ii) During the second period of the conditioning phase, the glass was maintained at 656°C for 8 hours (see Figure 1 12 in );

[0177] (iii) During the third period of the conditioning phase, the glass was cooled from 656°C to room temperature within 8 hours (see Figure 1 14 of 1999); and

[0178] (iv) In the fourth period of the conditioning phase, the dimensional change at the end of the third period is measured, for example, by a reference method.

[0179] The test procedure may also include a first measurement phase comprising:

[0180] (i) In the first period of the first measurement phase, the glass is heated from room temperature (e.g., 20° C.) to 656° C. (see Figure 1 10 in );

[0181] (ii) During the second period of the first measurement phase, the glass was kept at 656° C. for 6 minutes (see Figure 1 12 in );

[0182] (iii) In the third period of the first measurement phase, the glass was rapidly cooled from 656°C to room temperature (see Figure 1 14 of 1999); and

[0183] (iv) In the fourth period of the first measurement stage, the dimensional change at the end of the third period is measured.

[0184] The test program may include a second measurement phase, in which periods 1-4 of the first measurement phase are repeated, and may even include a third measurement phase.

[0185] Dimensional change can be measured in a variety of ways using commercially available or custom equipment. For example, dimensional change can be measured by drawing a reference line around the edge of the sample and then measuring the change in circumference using, for example, a Mitutoyo Apex vision system.

[0186] While the aforementioned test procedure does not capture true inviscid relaxation, as its magnitude is small even in large-format glass sheets, it can serve as an accurate proxy that does capture the relative inviscid behavior of the glass. The test procedure can provide a single value, denoted here as Nv, that represents this behavior, thereby providing a convenient metric that allows comparison of glass properties. The lower the Nv value, the lower the contribution of inviscid relaxation to TPV, and thus the lower the expected overall TPV value of that glass composition in downstream processing after manufacturing.

[0187] Those skilled in the art will recognize from this disclosure that testing procedures employing other times, temperatures, and numbers of measurement phase repetitions can be used to distinguish the effects of fast and slow relaxers, as long as the procedure employs a conditioning phase held at a preselected elevated temperature for a long period of time and a slow quenching rate, followed by a measurement phase using the same preselected temperature and a faster quenching rate.

[0188] In general, the conditioning phase of the test procedure is used to significantly reduce the contribution of slow relaxants to the dimensional changes measured in the measurement phase. Typically, glass samples will exhibit a dimensional change (compaction) of approximately 3300-1500ppm during the conditioning phase. In addition to turning off the slow relaxants, the conditioning phase also sets the fast relaxants to a low fictive temperature state so that they will expand in the measurement phase. The relative amount of expansion observed in the measurement phase can then be used as a measure of the fast relaxants present in the glass of interest. In other words, the amount of expansion that the glass experiences in the measurement phase represents the glass Nv peak expansion compared to the conditioning phase.

[0189] By reference Figure 2 and Figure 3 Understandable Figure 1 The ability of the procedure in to separate the behavior of slow and fast relaxers. Figure 2 The curves 22 and 24 of FIG. 1 respectively plot the fictive temperature of the slow relaxant and the fast relaxant over time during the test procedure. As shown in the figure, the first part of the test procedure (conditioning phase) turns off the slow relaxant, i.e., Figure 2 The curve 22 of is substantially flat at the end of the adjustment phase 26 and is substantially flat during the measurement phase (i.e., during the Figure 2 The surface of the substrate remains substantially flat during the heating-rapid quenching steps 28, 30 and 32.

[0190] Figure 3 The dimensional changes that occur during the measurement phase are shown. Specifically, curve 34 shows the dimensional changes due to the fast relaxant, curve 36 shows the dimensional changes due to the slow relaxant, and curve 38 shows the combined dimensional changes, which result in measured data points 40, 42 and 44, which can be averaged to provide a measure of the expansion peak of the glass. As shown in these curves, since the slow relaxant has been essentially turned off during the conditioning phase, the fast relaxant is able to produce significant observable expansion behavior during the measurement phase.

[0191] use Figures 1 to 3 The effect of compositional changes on fast relaxors can be determined by a test procedure. The method of enhancing the effect of fast relaxors by compositional changes can be applied to the study of compositions that minimize Nv. It is known in the art that, in general, display glasses contain SiO2 and Al2O3 as glass formers, and contain CaO, SrO and MgO as components that change the glass properties such as the CTE, strain point, annealing point, melting point, viscosity, etc. In addition to these components, the glass may also contain various other ingredients, such as B2O3, BaO, clarifiers, etc.

[0192] Therefore, Nv thermal cycling is used to evaluate many high performance display class compositions. Table 1 contains the composition by sample number (S#) in mole percent on an oxide basis, the measured Nv value (in ppm), and the annealing point (temperature) in degrees Celsius.

[0193] Table 1

[0194]

[0195]

[0196]

[0197]

[0198] In order to better understand the distribution of Nv values ​​in the space of interest, the Nv data obtained experimentally in Table 1 are used to construct a mathematical representation of the Nv variation in this space.

[0199] Once the complete dataset was obtained, it was split into training and test sets. Given the small size of the dataset, two models based on symbolic regression and Gaussian processes were constructed. For the symbolic regression model, a genetic algorithm was used to build and iteratively improve the prediction accuracy of a large cluster of models that could correctly predict Nv, which were represented by mathematical formulas. The best formula was selected from the trained cluster based on the best performance on the test set. Figure 4 A representation of the agreement between the predictions of the best model based on the genetic algorithm and the measured data is given. In order to have a high confidence in the predictions, we considered Gaussian processes, which represent a probability-based approach that computes the standard deviation during inference and based on the data distribution. The more a data point is surrounded by experimental neighbors, the higher the confidence in the prediction. Figures 5 and 6 The accuracy of this implementation is shown in . For each model, approximately 20% of the data was used for the test set. In symbolic regression, the size of the clusters and the maximum depth of the tree representing the formula were different. This helps to address the nonlinearity of Nv. For the Gaussian process, a Monte Carlo tree search was implemented that iteratively increased the complexity of the functions describing the covariance within the data, through intelligent combinations of basic covariance functions, up to four levels deep. Once accurate models were generated by each method, these models were used to predict a subset of compositions that were retained for validation. Due to the consistency between the predictions from the two models over the entire range of the data, the predictions from the Gaussian process were used because it also provided guidance with the variance of the predictions. Table 2 shows the composition range studied expressed in mole percentages on an oxide basis.

[0200] Table 2

[0201] <![CDATA[SiO2]]> <![CDATA[Al2O3]]> <![CDATA[B2O3]]> MgO CaO SrO BaO <![CDATA[TiO2]]> ZnO <![CDATA[Y2O3]]> <![CDATA[La2O3]]> <![CDATA[P2O5]]> 69.25 12.00 1.00 4.00 5.00 0.00 2.50 0.00 0.00 0.00 0.00 0.00 70.75 13.50 2.00 6.00 6.50 1.50 4.00 1.50 0.75 1.00 1.00 0.50

[0202] Over this composition range, the model is used to predict the Nv values ​​for each oxide in a grid of 0.25 mol percent steps. The set of glass compositions with Nv values ​​less than 16 ppm is then selected. From there, the space of glass compositions of interest is described by the convex hull, which is the smallest convex boundary that contains a set of points in a space of a given dimension.

[0203] The Nv values ​​produced by the Nv thermal cycle will be related to the glass manufacturing method used. This is at least due to the fact that the hydroxyl content ("water") in the glass can vary between processes, and high water content is believed to be a driver of inviscid relaxation. For example, a melt produced on one set of equipment may be drier than glass produced on another set of equipment. Therefore, Nv values ​​may vary even within the same composition. However, it was found that the model described in this paper can accurately capture Nv cycling values ​​even in the presence of water differences, indicating that the overall water concentration variation between melt systems is not sufficient to affect the ability to accurately model relative variations between glass compositions.

[0204] Glass compositions may include silicon dioxide (SiO2). Silicon dioxide acts as a primary glass former. Silicon dioxide may help increase liquidus viscosity, thereby protecting the glass composition from crystallization. However, the addition of SiO2 to the glass composition may cause liquid-liquid phase separation, thereby causing devitrification of the resulting glass and / or reducing the transmittance of the resulting glass. In addition, SiO2 is a low refractive index component, making it difficult to achieve high refractive index glass. In some embodiments, the glass may contain SiO2 in an amount greater than or equal to 69 mol.% to less than or equal to 72 mol.%, for example, in a range of about 69 mol.% to about 71.8 mol%, in a range of about 69 mol% to about 71.6 mol%, in a range of about 69 mol% to about 71.4 mol%, in a range of about 69 mol% to about 71.2 mol%, in a range of about 69 mol% to about 71 mol%, in a range of about 69 mol% to about 69.8 mol%, in a range of about 69 mol% to about 69.6 mol%, or in a range of about 69 mol% to about 69.4 mol%, including all ranges and sub-ranges therebetween. In further embodiments, the glass composition may contain SiO2 in an amount within a range of about 69.2 mol% to about 72 mol%, within a range of about 69.4 mol% to about 72 mol%, within a range of about 69.6 mol% to about 72 mol%, within a range of about 69.8 mol% to about 72 mol%, within a range of about 70.0 mol% to about 72 mol%, within a range of about 70.2 mol% to about 72 mol%, within a range of about 70.4 mol% to about 72 mol%, within a range of about 70.6 mol% to about 72 mol%, within a range of about 70.8 mol% to about 72 mol%, within a range of about 71 mol% to about 72 mol%, within a range of about 71.2 mol% to about 72 mol%, within a range of about 71.4 mol% to about 72 mol%, within a range of about 71.6 mol% to about 72 mol%, or within a range of about 71.8 mol% to about 72 mol%, including all ranges and subranges therebetween.

[0205] The glass compositions described herein include phosphorus oxide (P2O5) as a glass former. Large amounts of P2O5 increase the melt viscosity at a given temperature, thereby inhibiting crystallization of the melt upon cooling, thereby improving the glass forming ability of the melt (i.e., reducing the critical cooling rate of the melt). However, P2O5, when added to a glass composition, significantly reduces the refractive index, which makes it more difficult to achieve a high refractive index. Therefore, the P2O5 content in a high refractive index glass may be limited. In some embodiments, the glass may contain P2O5 in an amount equal to or less than about 1 mol.%, for example, equal to or less than about 0.75 mol.%, or equal to or less than about 0.5 mol.%, including all ranges and sub-ranges therebetween.

[0206] Glass compositions may include divalent metal oxides (RO). Divalent metal oxides, such as alkaline earth metal oxides (e.g., MgO, CaO, SrO, and BaO), zinc oxide (ZnO), cadmium oxide (CdO), lead oxide (PbO), etc., when added to glass, provide a relatively high refractive index, greater than the refractive index of most monovalent oxides. Some divalent metal oxides, such as, for example, CaO, SrO, and ZnO, also provide relatively low density, therefore, improving the ratio of refractive index to density, thereby improving the performance of optical glass in certain applications. In addition, divalent metal oxides may help to improve the solubility of high refractive index components (such as TiO2), which indirectly leads to a further increase in refractive index at comparable density. In addition, some divalent metal oxides, such as, for example, ZnO and MgO, have a relatively low coefficient of thermal expansion, which can reduce the thermal stress formed by glass products when cooling, thereby improving the quality of glass products. However, when the addition amount is high, divalent metal oxides may cause crystallization or liquid-liquid phase separation of refractory minerals in the melt, which may reduce the glass forming ability of the glass. Therefore, the amount of some divalent metal oxides in the glass compositions of the present disclosure may be limited.

[0207] The glass composition may include calcium oxide (CaO). Of the known monovalent and divalent metal oxides, calcium oxide provides the highest glass refractive index to density ratio. In addition, in some embodiments, CaO may help increase the solubility of Nb2O5 and TiO2, which additionally helps increase the refractive index at relatively low densities. In some embodiments, the glass may contain CaO in an amount greater than or equal to 0 mol% to less than or equal to 16 mol%, for example, in a range of about 0 mol% to about 15 mol%, in a range of about 0 mol% to about 14 mol%, in a range of about 0 mol% to about 13 mol%, in a range of about 0 mol% to about 12 mol%, in a range of about 0 mol% to about 11 mol%, in a range of about 0 mol% to about 10 mol%, in a range of about 0 mol% to about 9 mol%, in a range of about 0 mol% to about 8 mol%, in a range of about 0 mol% to about 7 mol%, in a range of about 0 mol% to about 6 mol%, in a range of about 0 mol% to about 5 mol%, in a range of about 0 mol% to about 4 mol%, in a range of about 0 mol% to about 3 mol%, in a range of about 0 mol% to about 2 mol%, or in a range of about 0 mol% to about 1 mol%, including all ranges and sub-ranges therebetween. In some embodiments, the glass composition may contain CaO in an amount ranging from about 1 mol% to about 16 mol%, for example, in a range of about 2 mol% to about 16 mol%, in a range of about 3 mol% to about 16 mol%, in a range of about 4 mol% to about 16 mol%, in a range of about 5 mol% to about 16 mol%, in a range of about 6 mol% to about 16 mol%, in a range of about 7 mol% to about 16 mol%, in a range of about 8 mol% to about 16 mol%, in a range of about 9 mol% to about 16 mol%, in a range of about 10 mol% to about 16 mol%, in a range of about 11 mol% to about 16 mol%, in a range of about 12 mol% to about 16 mol%, in a range of about 13 mol% to about 16 mol%, in a range of about 14 mol% to about 16 mol%, or in a range of about 15 mol% to about 16 mol%, including all ranges and sub-ranges therebetween.

[0208] The glass composition may include barium oxide (BaO). Barium oxide can increase the solubility of high refractive index components such as TiO2 above other divalent metal oxides, which may indirectly lead to a further increase in refractive index at a relatively low density. However, barium is a heavy element and its addition in large amounts may increase the density of the glass. In addition, at high concentrations, it may cause crystallization of minerals such as barium titanate (BaTiO3), barium niobate (BaNb2O6), and barium orthophosphate (Ba3P2O8), which may cause the melt to crystallize upon cooling. Thus, the amount of BaO in the glass of the present disclosure may contain barium oxide (BaO) in an amount of about 0 mol % to about 17.0 mol %, for example, in a range of about 1 mol % to about 17 mol %, in a range of about 2 mol % to about 17 mol %, in a range of about 3 mol % to about 17 mol %, in a range of about 4 mol % to about 17 mol %, in a range of about 5 mol % to about 17 mol %, in a range of about 6 mol % to about 17 mol %, in a range of about 7 mol % to about 17 mol %, in a range of about 8 mol % to about 17 mol %, or in a range of about 10 mol % to about 17 mol %. % within the range of about 9 mol % to about 17 mol %, within the range of about 10 mol % to about 17 mol %, within the range of about 11 mol % to about 17 mol %, within the range of about 12 mol % to about 17 mol %, within the range of about 13 mol % to about 17 mol %, within the range of about 14 mol % to about 17 mol %, within the range of about 15 mol % to about 17 mol %, within the range of about 16 mol % to about 17 mol %, including all ranges and subranges therebetween and all ranges and subranges between the foregoing values.

[0209] The glass composition can contain BaO in an amount ranging from about 0 mol% to about 16 mol%, for example, in a range of about 0 mol% to about 15 mol%, in a range of about 0 mol% to about 14 mol%, in a range of about 0 mol% to about 13 mol%, in a range of about 0 mol% to about 12 mol%, in a range of about 0 mol% to about 11 mol%, in a range of about 0 mol% to about 10 mol%, in a range of about 0 mol% to about 9 mol%, in a range of about 0 mol% to about 8 mol%, in a range of about 0 mol% to about 7 mol%, in a range of about 0 mol% to about 6 mol%, in a range of about 0 mol% to about 5 mol%, in a range of about 0 mol% to about 4 mol%, in a range of about 0 mol% to about 3 mol%, in a range of about 0 mol% to about 2 mol%, or in a range of about 0 mol% to about 1 mol%, including all ranges and sub-ranges therebetween.

[0210] The glass composition may include magnesium oxide (MgO). Magnesium oxide reduces the coefficient of thermal expansion, which may help reduce thermal stresses formed in the glass article when it is cooled. However, compared with other divalent metal oxides (such as, for example, BaO, SrO, CaO, and ZnO), magnesium oxide provides a lower refractive index and a lower increase in the solubility of high refractive index components. Therefore, the amount of MgO in the glass composition of the present disclosure may be limited, or the glass may be substantially free of MgO. In some embodiments, magnesium oxide (MgO) may be contained in the glass in an amount of about 0 mol.% to about 17 mol%, including all ranges and sub-ranges between the aforementioned values.

[0211] In some embodiments, the glass composition may contain MgO in a range of about 1 mol% to about 17 mol%, in a range of about 2 mol% to about 17 mol%, in a range of about 3 mol% to about 17 mol%, in a range of about 4 mol% to about 17 mol%, in a range of about 5 mol% to about 17 mol%, in a range of about 6 mol% to about 17 mol%, in a range of about 7 mol% to about 17 mol%, in a range of about 8 mol% to about 17 mol%, in a range of about 9 mol% to about 17 mol%, in a range of about 10 mol% to about 17 mol%, in a range of about 11 mol% to about 17 mol%, in a range of about 12 mol% to about 17 mol%, in a range of about 13 mol% to about 17 mol%, in a range of about 14 mol% to about 17 mol%, in a range of about 15 mol% to about 17 mol%, or in a range of about 16 mol% to about 17 mol%, including all ranges and sub-ranges therebetween.

[0212] The glass composition can contain MgO in an amount ranging from about 1 mol% to about 16 mol%, for example, in a range of about 1 mol% to about 15 mol%, in a range of about 1 mol% to about 14 mol%, in a range of about 1 mol% to about 13 mol%, in a range of about 1 mol% to about 12 mol%, in a range of about 1 mol% to about 11 mol%, in a range of about 1 mol% to about 10 mol%, in a range of about 1 mol% to about 9 mol%, in a range of about 1 mol% to about 8 mol%, in a range of about 1 mol% to about 7 mol%, in a range of about 1 mol% to about 6 mol%, in a range of about 1 mol% to about 5 mol%, in a range of about 1 mol% to about 4 mol%, in a range of about 1 mol% to about 3 mol%, or in a range of about 1 mol% to about 2 mol%, including all ranges and sub-ranges therebetween.

[0213] The glass composition can include strontium oxide (SrO) in an amount from about 0 mol% to about 16 mol%, for example, in a range from about 1 mol% to about 16 mol%, in a range from about 2 mol% to about 16 mol%, in a range from about 3 mol% to about 16 mol%, in a range from about 4 mol% to about 16 mol%, in a range from about 5 mol% to about 16 mol%, in a range from about 6 mol% to about 16 mol%, in a range from about 7 mol% to about 16 mol%, in a range from about 8 mol% to about 16 mol%, in a range from about 9 mol% to about 16 mol%, in a range from about 10 mol% to about 16 mol%, in a range from about 11 mol% to about 16 mol%, in a range from about 12 mol% to about 16 mol%, in a range from about 13 mol% to about 16 mol%, in a range from about 14 mol% to about 16 mol%, or in a range from about 15 mol% to about 16 mol%, including all ranges and subranges therebetween and all ranges and subranges between the foregoing values.

[0214] The glass composition can contain SrO in an amount ranging from about 1 mol% to about 15 mol%, from about 1 mol% to about 14 mol%, from about 1 mol% to about 13 mol%, from about 1 mol% to about 12 mol%, from about 1 mol% to about 11 mol%, from about 1 mol% to about 10 mol%, from about 1 mol% to about 9 mol%, from about 1 mol% to about 8 mol%, from about 1 mol% to about 7 mol%, from about 1 mol% to about 6 mol%, from about 1 mol% to about 5 mol%, from about 1 mol% to about 4 mol%, from about 1 mol% to about 3 mol%, or from about 1 mol% to about 2 mol%, including all ranges and sub-ranges therebetween.

[0215] In some embodiments, the glass composition may include ZnO in an amount in the range of about 0 mol % to about 1 mol %, such as in the range of about 0.25 mol % to about 1 mol %, in the range of about 0.5 mol % to about 1 mol %, or in the range of about 0.75 mol % to about 1 mol %, including all ranges and sub-ranges therebetween.

[0216] The glass composition may include aluminum oxide (Al2O3). Aluminum oxide may increase the viscosity of the glass-forming melt at high temperatures, which may reduce the critical cooling rate and improve the glass-forming ability. However, the addition of Al2O3 to high-refractive-index phosphate glasses may result in the crystallization of refractory minerals such as aluminum phosphate (AlPO4), aluminum titanate (Al2TiO5), aluminum niobate (AlNbO4) in the glass-forming melt during cooling. Therefore, the amount of Al2O3 in the glass of the present disclosure is limited, or the glass may be substantially free of Al2O3. In some embodiments, the glass may contain aluminum oxide (Al2O3) in an amount of about 11 mol% to about 15 mol%, for example, in the range of about 12 mol% to about 15 mol%, in the range of about 13 mol% to about 15 mol%, in the range of about 14 mol% to about 15 mol%, including all ranges and sub-ranges therebetween. The glass may contain aluminum oxide (Al2O3) in an amount of about 11 mol% to about 14 mol%, such as in the range of about 11 mol% to about 13 mol%, or in the range of about 11 mol% to about 12 mol%, including all ranges and sub-ranges therebetween.

[0217] The glass composition may include titanium dioxide (TiO2). High refractive index glasses typically include substances such as TiO2, which absorb at least a portion of visible light, especially light in the blue and near ultraviolet regions of the electromagnetic spectrum. In some embodiments, the glass may contain titanium dioxide (TiO2) in an amount from greater than or equal to 0 mol.% to about 2 mol%, for example, in a range of about 0.5 mol% to about 2 mol%, in a range of about 1 mol% to about 2 mol%, or in a range of about 1.5 mol% to about 2 mol%, including all ranges and sub-ranges therebetween.

[0218] In some embodiments, the glass may contain Y2O3 in an amount in the range of about 0 mol% to about 1 mol%, for example in the range of about 0.25 mol% to about 1 mol%, in the range of about 0.5 mol% to about 1 mol%, or in the range of about 0.75 mol% to about 1 mol%, including all ranges and sub-ranges therebetween.

[0219] In some embodiments, the glass may contain La2O3 in an amount in the range of about 0 mol% to about 1 mol%, for example in the range of about 0.25 mol% to about 1 mol%, in the range of about 0.5 mol% to about 1 mol%, or in the range of about 0.75 mol% to about 1 mol%, including all ranges and sub-ranges therebetween.

[0220] In some embodiments, the annealing point (temperature) of the glass may be equal to or greater than about 760°C, such as in the range of about 760°C to about 900°C, such as in the range of about 760°C to about 890°C, in the range of about 760°C to about 880°C, in the range of about 760°C to about 870°C, in the range of about 760°C to about 860°C, in the range of about 760°C to about 840°C, in the range of about 760°C to about 830°C, in the range of about 760°C to about 820°C, in the range of about 760°C to about 810°C, in the range of about 760°C to about 800°C, in the range of about 760°C to about 800°C, in the range of about 760°C to about 790°C, in the range of about 760°C to about 780°C, or in the range of about 760°C to about 770°C, including all ranges and sub-ranges therebetween.

[0221] In some embodiments, the annealing point of the glass may be in the range of about 770°C to about 900°C, such as in the range of about 780°C to about 900°C, in the range of about 790°C to about 900°C, in the range of about 800°C to about 900°C, in the range of about 810°C to about 900°C, in the range of about 820°C to about 900°C, in the range of about 830°C to about 900°C, in the range of about 840°C to about 900°C, in the range of about 850°C to about 900°C, in the range of about 860°C to about 900°C, in the range of about 870°C to about 900°C, in the range of about 880°C to about 900°C, or in the range of about 890°C to about 900°C, including all ranges and sub-ranges therebetween.

[0222] In some embodiments, a convex hull comprising an exemplary glass composition may be described, wherein the glass composition comprises:

[0223] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0224] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0225] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0226] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0227] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0228] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0229] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0230] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0231] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0232] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0233] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0234] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0235] The glass meets the following conditions:

[0236] where the symbol "*" represents multiplication, and

[0237] Intercept = -11.20751259, the coefficient Xi of the component oxide is:

[0238] SiO2=-0.002926308,

[0239] Al2O3=-0.004673511,

[0240] B2O3=-0.001118634,

[0241] MgO=1.126496816,

[0242] CaO=1.615716878,

[0243] SrO = 3.063872526,

[0244] BaO=1.551023535,

[0245] TiO2=-0.004673511,

[0246] ZnO=0,

[0247] Y2O3=-0.001118634,

[0248] La2O3 = -0.001118634, and

[0249] P2O5=-2.235863244.

[0250] The intercepts and coefficients Xi for the various component oxides are listed above, while the values ​​Yi are the corresponding mol% concentrations. The oxides can be divided into three groups, namely V1, V2 and V3, where:

[0251] V1=SiO2+Al2O3+B2O3

[0252] V2=MgO+CaO+BaO+SnO2

[0253] V3=TiO2+ZnO+La2O3+La2O3+P2O5, and among them

[0254] V1 is in the range of 82.25 to 86.25,

[0255] V2 is in the range of 13.00 to 17.50, and

[0256] V3 is in the range of 0.00 to 4.75.

[0257] Figure 7 A graphical representation of the convex hull is shown in . The boundary points of the convex hull are provided in Table 3 below.

[0258] Table 3

[0259]

[0260]

[0261] In other embodiments, another convex hull comprising an exemplary glass composition may be described, the glass composition comprising:

[0262] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0263] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0264] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0265] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0266] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0267] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0268] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0269] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0270] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0271] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0272] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0273] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0274] The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -234.7571088, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0275] SiO2=2.232090497,

[0276] Al2O3=2.230475478,

[0277] B2O3=2.233717001,

[0278] MgO=3.368563490,

[0279] CaO=3.851331728,

[0280] SrO = 5.301366502,

[0281] BaO=3.788612774,

[0282] TiO2=2.230475478,

[0283] ZnO=2.23468972,

[0284] Y2O3=2.233717001,

[0285] La2O3=2.233717001, and

[0286] P2O5=0.

[0287] The intercepts and coefficients Xi for the various component oxides are listed above, while the value Yi is the corresponding mole percent concentration. The oxides can be divided into three groups, namely V1, V2 and V3, where:

[0288] V1=SiO2+Al2O3+B2O3

[0289] V2=MgO+CaO+BaO+SnO2

[0290] V3=TiO2+ZnO+La2O3+La2O3+P2O5, and among them

[0291] V1 is in the range of 82.25 to 86.25,

[0292] V2 is in the range of 13.00 to 17.50, and

[0293] V3 is in the range of 0.00 to 4.75.

[0294] Figure 8 A graphical representation of the convex hull is shown in . The boundary points of the convex hull are provided in Table 4 below.

[0295] Table 4

[0296]

[0297]

[0298] In yet other embodiments, another convex hull comprising an exemplary glass composition may be described, the glass composition comprising:

[0299] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0300] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0301] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0302] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0303] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0304] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0305] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0306] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0307] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0308] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0309] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0310] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0311] The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -237.7578217, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0312] SiO2=2.25149345,

[0313] Al2O3=2.250724382,

[0314] B2O3=2.252392713,

[0315] MgO=3.524128464,

[0316] CaO=3.890462587,

[0317] SrO = 5.366534992,

[0318] BaO=3.897785139,

[0319] TiO2=2.250724382,

[0320] ZnO=2.253175066,

[0321] Y2O3=2.252392713,

[0322] La2O3=2.252392713, and

[0323] P2O5=0.

[0324] The intercepts and coefficients Xi for the various component oxides are listed above, while the value Yi is the corresponding mole percent concentration. The oxides can be divided into three groups, namely V1, V2 and V3, where:

[0325] V1=SiO2+Al2O3+B2O3

[0326] V2=MgO+CaO+BaO+SnO2

[0327] V3=TiO2+ZnO+La2O3+La2O3+P2O5, and among them

[0328] V1 is in the range of 82.25 to 86.25

[0329] V2 in the range of 13.00 to 17.50

[0330] V3 in the range of 0.00 to 4.75

[0331] Fig. 9 A graphical representation of the convex hull is shown in . The boundary points of the convex hull are provided in Table 5 below.

[0332] Table 5

[0333]

[0334]

[0335] In yet other embodiments, another convex hull comprising an exemplary glass composition may be described, the glass composition comprising:

[0336] greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2,

[0337] greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3,

[0338] 1.00 mol.% or more and 2.00 mol.% or less of B2O3,

[0339] MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%,

[0340] greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO,

[0341] 0.00 mol.% or more and 1.50 mol.% or less of SrO,

[0342] 2.50 mol.% or more and 4.00 mol.% or less of BaO,

[0343] greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2,

[0344] greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO,

[0345] 0.00 mol.% or more and 1.00 mol.% or less of Y2O3,

[0346] greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3,

[0347] 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and

[0348] The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -242.7132028, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is:

[0349] SiO2=2.260131924,

[0350] Al2O3=2.260271613,

[0351] B2O3=2.26056072,

[0352] MgO=3.878171611,

[0353] CaO=4.168656199,

[0354] SrO=5.552077225,

[0355] BaO=4.212721511,

[0356] TiO2=2.260271613,

[0357] ZnO=2.259907435,

[0358] Y2O3=2.26056072,

[0359] La2O3=2.26056072, and

[0360] P2O5=0.

[0361] The intercepts and coefficients Xi for the various component oxides are listed above, while the value Yi is the corresponding mole percent concentration. The oxides can be divided into three groups, namely V1, V2 and V3, where:

[0362] V1=SiO2+Al2O3+B2O3

[0363] V2=MgO+CaO+BaO+SnO2

[0364] V3=TiO2+ZnO+La2O3+La2O3+P2O5, and among them

[0365] V1 is in the range of 82.25 to 86.25

[0366] V2 in the range of 13.00 to 17.50

[0367] V3 in the range of 0.00 to 4.75

[0368] Fig.10 A graphical representation of the convex hull is shown in . The boundary points of the convex hull are provided in Table 6 below.

[0369] Table 6

[0370]

[0371]

[0372] Fig.11 It is shown Figures 7 to 10 Plots of the convex hulls shown in , nested in the same plot.

[0373] Given a composition defined by all oxides listed in Table 2, to test whether the composition belongs to the exemplary convex hull, the following steps can be followed:

[0374] Projecting this composition into the reduced space, the coordinates are as follows:

[0375] a.V1=SiO2+Al2O3+B2O3

[0376] b. V2=MgO+CaO+SrO+BaO

[0377] c.V3=TiO2+ZnO+La2O3+P2O5+Y2O3

[0378] run The distributed code,

[0379] inhul(P,K) where K is the set of boundary points that depend on the convex hull being tested.

[0380] If the response is 0, then point K is not within the space bounded by K.

[0381] If the response is 1, then point K is in the space bounded by K

[0382] It will be apparent to those skilled in the art that various modifications and changes can be made to the embodiments of the present disclosure without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is intended to cover such modifications and changes as long as they fall within the scope of the appended claims and their equivalents.

Claims

1. A glass comprising a plurality of components, wherein the composition of the components of the glass comprises, based on oxides: greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2, greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3, 1.00 mol.% or more and 2.00 mol.% or less of B2O3, MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%, greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO, 0.00 mol.% or more and 1.50 mol.% or less of SrO, 2.50 mol.% or more and 4.00 mol.% or less of BaO, greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2, greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO, 0.00 mol.% or more and 1.00 mol.% or less of Y2O3, greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3, 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -11.20751259, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is: SiO2=-0.002926308, Al2O3=-0.004673511, B2O3=-0.001118634, MgO=1.126496816, CaO=1.615716878, SrO = 3.063872526, BaO=1.551023535, TiO2=-0.004673511, ZnO=0, Y2O3=-0.001118634, La2O3=-0.001118634, P2O5 = -2.235863244; and in, SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%, MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

2. A glass comprising a plurality of components, wherein the composition of the components of the glass comprises, based on oxides: greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2, greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3, 1.00 mol.% or more and 2.00 mol.% or less of B2O3, MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%, greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO, 0.00 mol.% or more and 1.50 mol.% or less of SrO, 2.50 mol.% or more and 4.00 mol.% or less of BaO, greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2, greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO, 0.00 mol.% or more and 1.00 mol.% or less of Y2O3, greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3, 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -234.7571088, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is: SiO2=2.232090497, Al2O3=2.230475478, B2O3=2.233717001, MgO=3.368563490, CaO=3.851331728, SrO = 5.301366502, BaO=3.788612774, TiO2=2.230475478, ZnO=2.23468972, Y2O3=2.233717001, La2O3=2.233717001, P2O5=0; and in, SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%, MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

3. A glass comprising a plurality of components, wherein the composition of the components of the glass comprises, based on oxides: greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2, greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3, 1.00 mol.% or more and 2.00 mol.% or less of B2O3, MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%, greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO, 0.00 mol.% or more and 1.50 mol.% or less of SrO, 2.50 mol.% or more and 4.00 mol.% or less of BaO, greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2, greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO, 0.00 mol.% or more and 1.00 mol.% or less of Y2O3, greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3, 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -237.7578217, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is: SiO2=2.25149345, Al2O3=2.250724382, B2O3=2.252392713, MgO=3.524128464, CaO=3.890462587, SrO = 5.366534992, BaO=3.897785139, TiO2=2.250724382, ZnO=2.253175066, Y2O3=2.252392713, La2O3=2.252392713, P2O5=0; and in, SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%, MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

4. A glass comprising a plurality of components, wherein the composition of the components of the glass comprises, based on oxides: greater than or equal to 69.25 mol.% and less than or equal to 70.75 mol.% SiO2, greater than or equal to 12.00 mol.% and less than or equal to 13.50 mol.% of Al2O3, 1.00 mol.% or more and 2.00 mol.% or less of B2O3, MgO greater than or equal to 4.00 mol.% and less than or equal to 6.00 mol.%, greater than or equal to 5.00 mol.% and less than or equal to 6.50 mol.% CaO, 0.00 mol.% or more and 1.50 mol.% or less of SrO, 2.50 mol.% or more and 4.00 mol.% or less of BaO, greater than or equal to 0.00 mol.% and less than or equal to 1.50 mol.% TiO2, greater than or equal to 0.00 mol.% and less than or equal to 0.75 mol.% of ZnO, 0.00 mol.% or more and 1.00 mol.% or less of Y2O3, greater than or equal to 0.00 mol.% and less than or equal to 1.00 mol.% La2O3, 0.00 mol.% or more and 0.50 mol.% or less of P2O5; and The glass meets the following conditions: Where the symbol "*" indicates multiplication, the intercept = -242.7132028, the value Yi is the amount of the oxide component in mol%, and the coefficient Xi is: SiO2=2.260131924, Al2O3=2.260271613, B2O3=2.26056072, MgO=3.878171611, CaO=4.168656199, SrO=5.552077225, BaO=4.212721511, TiO2=2.260271613, ZnO=2.259907435, Y2O3=2.26056072, La2O3=2.26056072, P2O5=0; and in, SiO2+Al2O3+B2O3 is in the range of 82.25mol% to 86.25mol%, MgO+CaO+BaO+SnO2 is in the range of 13.00mol% to 17.50mol%, and TiO2+ZnO+La2O3+La2O3+P2O5 is in the range of 0.00mol% to 4.75mol%.

Images