Abstract:
Described herein are alkali-free, boroalumino silicate glasses exhibiting desirable physical and chemical properties for use as substrates in flat panel display devices, such as, active matrix liquid crystal displays (AMLCDs) and active matrix organic light emitting diode displays (AMOLEDs). In accordance with certain of its aspects, the glasses possess good dimensional stability as a function of temperature. The glasses comprise in mol percent on an oxide basis: 70-74.5 SiO2, 10.5-13.5 AL2O3, 0-2.5 B2O3, 3-7 MgO, 3-7 CaO, 0-4 SrO, 1.5-6 BaO, 0-0.3 SnO2, 0-03 CeO2, 0-0.5 As2O3, 0-0.5 Sb2O3, 0.01-0.08 Fe2O3 and F+Cl+Br         RO/Al2O3         1.7 and 0.2         MgO/RO

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of priority under 35 U.S.C. §119 of U.S. Provisional Application Ser. No. 61/435,987 filed on Jan. 25, 2011, the content of which is hereby incorporated by reference. 
     
    
     BACKGROUND 
       [0002]    The production of liquid crystal displays such as, for example, active matrix liquid crystal display devices (AMLCDs) is very complex, and the properties of the substrate glass are extremely important. First and foremost, the glass substrates used in the production of AMLCD devices need to have their physical dimensions tightly controlled. The downdraw sheet drawing processes and, in particular, the fusion process described in U.S. Pat. Nos. 3,338,696 and 3,682,609, both to Dockerty, are capable of producing glass sheets that can be used as substrates without requiring costly post-forming finishing operations such as lapping and polishing. Unfortunately, the fusion process places rather severe restrictions on the glass properties, which require relatively high liquidus viscosities. 
         [0003]    In the liquid crystal display field, thin film transistors (TFTs) based on poly-crystalline silicon are preferred because of their ability to transport electrons more effectively. Poly-crystalline based silicon transistors (p-Si) are characterized as having a higher mobility than those based on amorphous-silicon based transistors (a-Si). This allows the manufacture of smaller and faster transistors. P-Si displays are at the core of state-of-the-art handheld devices. The p-Si thin film transistor array consumes very low power, permits very fine features (critical for small displays), and provides high brightness. 
         [0004]    The process used to make p-Si TFTs invariably includes a thermal excursion to quite high temperature to encourage the silicon to crystallize. In some processes, temperature alone is used to produce crystallization, and in such processes the peak temperatures are very high, very typically greater than 650° C. compared to the 350° C. peak temperatures employed in the manufacture of a-Si transistors. At these temperatures, most AMLCD glass substrates undergo a process known as compaction and will deform excessively unless supported from below. Compaction, also referred to as thermal stability or dimensional change, is an irreversible dimensional change (shrinkage or expansion) in the glass substrate due to changes in the glass&#39; fictive temperature. The magnitude of compaction depends both on the process by which a glass is made and the viscoelastic properties of the glass. In the float process for producing sheet products from glass, the glass sheet is cooled relatively slowly from the melt and, thus, “freezes in” a comparatively low temperature structure into the glass. The fusion process, by contrast, results in very rapid quenching of the glass sheet from the melt, and freezes in a comparatively high temperature structure. As a result, a glass produced by the float process possesses less compaction when compared to glass produced by the fusion process. In the glass product itself, the compaction ultimately may produce poor registry with the color filter and, if large enough, adversely affect device performance. Thus, it would be desirable to minimize the level of compaction in a glass substrate that is produced by a downdraw process. A commercial glass product, Jade® (Corning Incorporated, Corning N.Y.), was developed expressly to address this problem. It has a very high annealing point compared to conventional amorphous silicon substrate glasses, and thus shows low compaction even when reheated above the strain point of conventional amorphous silicon substrates. 
         [0005]    While the Jade® product has proven sufficient for many p-Si processes, there is still a demand for even lower levels of compaction and/or the capability of withstanding heat treatments at even higher temperatures, sometimes in excess of 700° C. Annealed low annealing point p-Si substrate glasses can be optimized to provide these lower levels of compaction but their deformation at elevated temperature is only marginally improved with this increased anneal. The Jade® product has better deformation at elevated temperatures than annealed low annealing point glasses but has too much compaction for some applications and may need even more resistance to deformation under the extreme conditions of some newly developed cycles. In order to provide the desired lower compaction in existing processes as well as enabling the development of new higher temperature processes, a glass with an annealing point in excess of 785° C. is desired. 
       SUMMARY 
       [0006]    In accordance with the purposes of the disclosed materials, compounds, compositions, articles, devices, and methods, as embodied and broadly described herein are alkali-free, boroalumino silicate glasses exhibiting desirable physical and chemical properties for use as substrates in flat panel display devices, such as, active matrix liquid crystal displays (AMLCDs) and active matrix organic light emitting diode displays (AMOLEDs). In accordance with certain of its aspects, the glasses possess good dimensional stability as a function of strain point. Specifically, the glasses described herein are fusion-compatible glasses with an anneal point in excess of 785° C., with a temperature at 200 poise of 1730° C. or less, with a density less than 2.65 g/cc, and with etch rates in fluoride-based mineral acids within 10% of the range exhibited by conventional a-Si substrate materials. Additional advantages will be set forth in part in the description that follows, and in part will be obvious from the description, or may be learned by practice of the aspects described below. The advantages described below will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]    The accompanying figures, which are incorporated in and constitute a part of this specification, illustrate several aspects described below. 
           [0008]      FIG. 1  is a comparison of the compaction of a glass typical of this invention with typical p-Si glasses. 
           [0009]      FIG. 2  shows thermal sag (measured as “Deflection” in the y-axis) at 700° C. of commercially available p-Si glasses relative to glasses typical of this invention. It is clear the GBII glass has superior sag behavior at 700° C. than either other p-Si glass, thereby enabling higher temperature thermal cycles in customers&#39; processes. 
           [0010]      FIG. 3  illustrates the (SiO 2 +Al 2 O 3 )/(1-B 2 O 3 ) vs. RO—Al 2 O 3 , in mole-% for glasses of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0011]    The materials, compounds, compositions, articles, devices, and methods described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein and to the Figures. 
         [0012]    Before the present materials, compounds, compositions, articles, devices, and methods are disclosed and described, it is to be understood that the aspects described below are not limited to specific synthetic methods or specific reagents, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting. 
         [0013]    Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon. 
         [0014]    Throughout the description and claims of this specification the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps. 
         [0015]    Certain materials, compounds, compositions, and components disclosed herein can be obtained commercially or readily synthesized using techniques generally known to those of skill in the art. For example, the starting materials and reagents used in preparing the disclosed compounds and compositions are either available from commercial suppliers or prepared by methods known to those skilled in the art. 
         [0016]    Also, disclosed herein are materials, compounds, compositions, and components that can be used for, can be used in conjunction with, can be used in preparation for, or are products of the disclosed methods and compositions. These and other materials are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these materials are disclosed that while specific reference of each various individual and collective combinations and permutation of these compounds may not be explicitly disclosed, each is specifically contemplated and described herein. 
         [0017]    Reference will now be made in detail to specific aspects of the disclosed materials, compounds, compositions, articles, and methods, examples of which are illustrated in the accompanying Examples and Figures. 
         [0018]    Described herein are alkali-free glasses and methods for making the same that possess high strain points and, thus, good dimensional stability (i.e., low compaction). A high strain point glass can prevent panel distortion due to compaction/shrinkage during thermal processing subsequent to manufacturing of the glass. 
         [0019]    The compositions represented by ranges of the present disclosure comprise SiO 2 , Al 2 O 3 , B 2 O 3 , MgO, CaO, SrO and BaO, and fining agents may include tin oxide (SnO 2 ), iron oxide (Fe 2 O 3 ), cerium oxide (CeO 2 ) various halides (principally F, Cl and Br), As 2 O 3  or Sb 2 O 3 . In one embodiment, the composition comprises an alkali-free glass comprising in mol percent on an oxide basis: 
         [0000]      70≦SiO 2 ≦74.5
 
         [0000]      10.5≦Al 2 O 3 ≦13.5
 
         [0000]      0≦B 2 O 3 ≦2.5
 
         [0000]      3≦MgO≦7
 
         [0000]      3≦CaO≦7
 
         [0000]      0≦SrO≦4
 
         [0000]      1.5≦BaO≦6
 
         [0000]      0≦SnO 2 ≦0.3
 
         [0000]      0≦CeO 2 ≦0.3
 
         [0000]      0≦As 2 O 3 ≦0.5
 
         [0000]      0≦Sb 2 O 3 ≦0.5
 
         [0000]      0.01≦Fe 2 O 3 ≦0.08
 
         [0000]      F+Cl+Br≦0.4
 
         [0000]      wherein 
         [0000]      1.05≦(MgO+CaO+SrO)/Al 2 O 3 ≦1.7  a)
 
         [0000]      0.2≦MgO/(MgO+CaO+SrO+BaO)≦0.45  b)
 
         [0000]    where Al 2 O 3 , MgO, CaO, SrO and BaO represent the mol percents of the representative oxide components. In another embodiment, the MgO/RO: is 0.29≦MgO/(MgO+CaO+SrO+BaO)≦0.39. 
         [0020]    In one embodiment, the compositions are further constrained as follows: 
         [0000]      SiO 2 +Al 2 O 3 =86.97−0.713*(MgO+CaO+SrO+BaO—Al 2 O 3 )±0.8
 
         [0021]    In another embodiment, glasses within the disclosed ranges are substantially free of arsenic oxide (As 2 O 3 ) or antimony oxide (Sb 2 O 3 ) such that the concentration of either or both of these oxides is less than 0.05 wt %. When this is the case, it may be preferable to add other multivalent oxides such as SnO 2 , Fe 2 O 3  and/or CeO 2  to ensure a minimum number of gaseous inclusions in the final glass. 
         [0022]    In one embodiment, the glasses of the present disclosure exhibit a density less than 2.65 g/cc. In another embodiment the glasses exhibit densities of less than 2.6 g/cc. 
         [0023]    Compositions falling within the above defined ranges are shown in Table 1. 
         [0024]    The temperature corresponding to 200 poise is often used as a rough guideline for the appropriate melting temperature of a glass. The 200 poise temperatures of the glasses in Table 1 are, for the most part, very high, generally greater than about 1670° C. A surprising result obtained for the inventive glasses is that at the low B 2 O 3  contents of the inventive ranges, the melting rate of the most refractory batch materials, notably SiO 2  (or sand), is accelerated relative to glasses with higher B 2 O 3  contents. Because of this, and because of the comparatively low resistivity of these glasses compared to glasses with higher B 2 O 3  contents, when the inventive glasses are melted in a joule-boosted CU melter with a platinum finer and optical stirrer, excellent glass quality is obtained for melter temperatures anywhere between about 200 and 450 poise. 
         [0025]    The temperature corresponding to 35,000 poise viscosity is regarded as a metric for the temperature at which glass is delivered to the trough of the isopipe. It is generally desirable that this temperature be as low as possible to minimize creep of the isopipe refractory over time. The inventive glasses generally have 35,000 poise temperatures between about 1280° C. and 1345° C., but at the high end of this range, it might be necessary to use a special refractory for the isopipe to obtain acceptable isopipe lifetime. Therefore, in one embodiment, the inventive glasses have 35,000 poise temperatures less than 1320° C., and in another embodiment, less than 1310° C. 
         [0026]    Fusion-drawn glass has a high fictive temperature, and this results in a substantial disequilibrium of the glass structure when reheated to temperatures close to the annealing point. If as-drawn glass is to be used in a p-Si process, the only means to minimize compaction are to anneal the glass at a temperature close to the annealing point, and thereby partially or entirely structurally relax the glass, or to increase the anneal point of the glass such that the rate of structural relaxation is reduced, and the magnitude of structural relaxation in the p-Si process is minimized. Unfortunately, the annealing point required to produce low levels of compaction in p-Si processes depends upon the details of the process, and is difficult to predict without running glasses with a variety of annealing points through the thermal cycle of interest. In general, to provide a consistent product to customers with different p-Si processes, the best means to minimize compaction is to make the annealing point as high as reasonably achieved consistent with manufacturability and other customer-related constraints. The inventive glasses have annealing temperatures greater than about 790° C., greater than any commercially-available substrate for AMLCD applications, and thus are great enough to produce minimal compaction in p-Si processes. In another embodiment, the annealing temperature exceeds 800° C. In yet another embodiment the annealing temperature exceeds 810° C. In another embodiment the annealing temperature exceeds 815° C. 
         [0027]    Each oxide constituent in the inventive glasses serves an important purpose. Silica, or SiO 2 , is the primary glass forming oxide, and contributes viscosity to the molten glass. For a given liquidus temperature, increasing viscosity serves to increase liquidus viscosity, and thus to improve compatibility with the fusion process. However, if viscosity becomes too high, then melting-related defects such as fining bubbles may appear, and erosion of refractories and degradation of platinum may become too extreme to permit long-term manufacturing in a continuous process. Furthermore, as silica increases, the liquidus temperature may increase due to increasing stability of cristobalite, a crystalline polymorph of SiO 2  that is an undesirable devitrification phase in a continuous process. Compared to every oxide except boron oxide (B 2 O 3 ), SiO 2  decreases density and coefficient of thermal expansion, and relative to B 2 O 3  it improves durability. SiO 2  ranges between 70 and 74.5 mol % in the inventive glasses. 
         [0028]    Aluminum oxide, or Al 2 O 3 , also serves as a glass former in the inventive glasses. Like SiO 2 , it contributes viscosity, and when carefully balanced against SiO 2  concentration and the relative and absolute concentrations of alkaline earths, can be used to reduce liquidus temperature, thus enhancing liquidus viscosity. An increase in Al 2 O 3  relative to every oxide except SiO 2  results in improved durability in the kinds of acid-based etchants commonly used to etch display glasses in amorphous-silicon-based etching processes. Like SiO 2 , an increase in Al 2 O 3  relative to the alkaline earths generally results in decreased density, decreased coefficient of thermal expansion, and improved durability. Of particular importance, increasing Al 2 O 3  at the expense of any component save SiO 2  will generally increase the anneal point, and thus a minimum amount of Al 2 O 3  is required to obtain the high anneal points required for the p-Si application. Because of the need to balance Al 2 O 3  against other oxides, the full range of Al 2 O 3  content of the inventive glasses is between 10.5 and 13.5 mol %. 
         [0029]    Boron oxide, or B 2 O 3 , is also a glass-forming oxide, and is used to reduce viscosity and, more importantly, to reduce liquidus temperature. In general, an increase in B 2 O 3  of 1 mol % decreases the temperature at equivalent viscosity by 10-14° C., depending on the details of the glass composition and the viscosity in question. However, B 2 O 3  can lower liquidus temperature by 18-22° C. per mol %, and thus has the effect of decreasing liquidus temperature more rapidly than it decreases viscosity, thereby increasing liquidus viscosity. As one moves to extremely low B 2 O 3  contents, keeping all other oxides within their respective ranges, it generally becomes increasingly difficult to obtain a liquidus viscosity as high as 130 kpoise, or more preferably greater than 170 kpoise, a prerequisite for compatibility with the fusion process as practiced today. If one were to increase boron oxide concentration at the expense of other glass components, CTE and density will generally decrease, but anneal point will decrease sharply, by as much as 14° C. per mol %, which is highly detrimental for p-Si substrate applications. On the other hand, relative to the other components that can reduce viscosity, principally the alkaline earth oxides, increasing boron oxide actually improves durability in fluoride-containing acids, making the glass more compatible with etching processes designed for amorphous silicon substrate glasses. For these reasons, B 2 O 3  is preferably kept between 0 and 2.5 mol %. In one embodiment, the glass is essentially free of B 2 O 3 . 
         [0030]    A surprising discovery is that glasses with comparatively low liquidus temperatures—and hence high liquidus viscosities—can be obtained in boron-free glasses. As noted above, boron oxide decreases liquidus temperature more rapidly than it decreases viscosity, so in general additions of B 2 O 3  improve liquidus viscosity. Furthermore, boron tends to reduce the composition dependence of liquidus temperature, such that a change in the relative concentration of a particular oxide in a boron-free glass will tend to cause a larger change to liquidus temperature than a change in a boron-containing glass. The unexpected result described herein is that for a narrow range of oxides other than B 2 O 3 , low liquidus temperatures can be obtained, and as these glasses are very viscous for reasons stated above, the corresponding liquidus viscosities can be very high and appropriate for the fusion process. For example, the liquidus viscosities of the glasses in Table 1 are about 130,000 poise or more, thus making them compatible with the fusion process. In addition, the fusion process operates over a particular range of viscosity: glass is delivered to the trough of the isopipe at a viscosity corresponding to 20,000-35,000 poise, and glass leaves the root of the isopipe in the form of a viscous ribbon at a viscosity corresponding to 100,000 poise or more. At the very high delivery temperatures of the inventive glasses, the rate of radiative heat loss is greater per unit area than for less viscous glasses simply because a substantial fraction of the black body radiation of the glass is at visible and near-infrared wavelengths, at which wavelengths the glass is substantially transparent. Therefore, practical implementation of the inventive glasses in the fusion process may require high liquidus viscosities compared to those that might otherwise work for amorphous silicon substrate glasses. Thus, in one embodiment, the glass composition has a liquidus viscosity of at least 170,000 poise. 
         [0031]    Alkaline earth oxides, MgO, CaO, SrO and BaO, are essential constituents for manufacturing. Like B 2 O 3 , increasing alkaline earths relative to SiO 2  or Al 2 O 3  always decreases the viscosity of a glass melt at fixed temperature. Since high temperature is the main factor limiting the lifetimes of glass tanks and forming equipment, it is always desirable to reduce melting and forming temperatures as much as possible consistent with delivering an appropriate suite of glass properties to a customer. Unlike SiO 2 , Al 2 O 3  and B 2 O 3 , increases in alkaline earths relative to the glass forming components generally degrade properties that are important for p-Si applications: CTE and density generally increase as alkaline earth oxides increase relative to SiO 2 , Al 2 O 3  and B 2 O 3 , anneal point generally decreases, and durability moves increasingly far from standard amorphous silicon substrate glasses. The only final glass properties that benefits from higher alkaline earth concentration is Young&#39;s modulus, and for some combinations of alkaline earth increases, specific modulus. Young&#39;s modulus determines the stiffness of a sheet of glass, and thus making it as high as possible is valuable for glass handling. At fixed temperature, the sag of a sheet of glass with widely spaced supports beneath it is dictated by the specific modulus, or the ratio of Young&#39;s modulus and density. High alkaline earth concentrations generally increase density, and so work against the expected increase in Young&#39;s modulus. However, MgO and CaO increase density much more slowly than the large alkaline earths, Sr and Ba, and thus the relative proportions of the alkaline earths can be manipulated to obtain an optimal combination of Young&#39;s modulus and density, consistent with fusion compatibility. In one embodiment, the specific modulus is greater than 30 GPa cm 3 /gm. In another embodiment, the specific modulus is greater than 31 GPa cm 3 /gm. In yet another embodiment, the specific modulus is greater than 31.5 GPa cm 3 /gm. 
         [0032]    Mixtures of alkaline earths are also required to obtain low liquidus temperatures. The reasons behind this are complex. Without wishing to be bound by theory, the inventive ranges for the various alkaline earths have the effect of putting two or more crystalline phases on the liquidus for most glasses within the inventive ranges, one of which is cristobalite (SiO 2 ), and one of which is an alkaline earth aluminosilicate. In barium-rich glasses, the alkaline earth aluminosilicate is often hexacelsian and solid solutions therein, expressed approximately as Ba 1−x−y ,Sr x ,Ca y Mg z Al 2−z Si 2+z O 8 , where x, y and z are generally less than 0.5. In glasses with low barium concentrations, and thus correspondingly high CaO+SrO concentrations, the alkaline earth aluminosilicate is often anorthite or solid solutions therein, expressed approximately as Ca 1−x−y Sr x Ba y Al 2 Si 2 O 8 . For Mg-rich compositions, the liquidus phase is sometimes cordierite or solid solutions therein, approximately Mg 2 Al 4 Si 5 O 18 . The best liquidus temperatures are generally obtained when two or more different aluminosilicate phases and cristobalite are on or close to the liquidus temperature. The relative competition of each phase for glass constituents has the effect of destabilizing other phases, and thus reduces not only the liquidus temperature, but the tendency to devitrify when undercooled in a manufacturing process. 
         [0033]    At a fixed level of alkaline earth oxides, melting and forming temperatures are generally reduced when Ba, Sr or Ca is replaced with Mg. This is particularly important when (MgO+CaO+SrO+BaO)/Al 2 O 3  (also referred to as RO/Al 2 O 3 ) is close to 1.0, as their high melt temperatures may make them almost impossible to melt. However, MgO is a participant in hexacelsian and cordierite, and at low (MgO+CaO+SrO+BaO)/Al 2 O 3  may stabilize mullite. Therefore, MgO needs to be confined to a narrow range of the total alkaline earth oxide concentration to obtain the best balance of viscosity and liquidus temperature: the molar ratio MgO/(MgO+CaO+SrO+BaO) is preferably kept in the range 0.2 to 0.45. In another embodiment this molar ratio is kept in the range of 0.29 to 0.39. In yet another embodiment, this molar ratio is kept in the range of 0.31 to 0.35. 
         [0034]    The alkaline earth oxide with the greatest beneficial impact on liquidus temperature is barium oxide, BaO. Unfortunately, it also has the effect of increasing melting and delivery temperatures when substituted for any other alkaline earth oxide, and compromises final glass properties such as density, CTE and anneal point more so than any other alkaline earth oxide. Strontium oxide, SrO, can be increased at the expense of barium to offset some of these deleterious effects, but with much diminished benefit to liquidus temperature. Because hexacelsian is substantially a barium-strontium aluminosilicate, with comparatively low CaO and BaO, it is generally desirable to have CaO concentrations comparable to the combined concentration of BaO+SrO. As a result of these considerations, the inventive glass will have BaO between 1.5 and 6 mol %, SrO between 0 and 4 mol %, and CaO between 3 and 7 mol %. Compositions within these limits have attractive physical properties and liquidus viscosities suitable for down draw processes such as the fusion process. 
         [0035]    Even if the melting temperature is comparatively low, the details of the melting equipment may make it difficult to clear gaseous inclusions from a glass melt. Those that remain appear as defects in the final ware. P—Si TFT manufacturers are extremely sensitive to defects that distort the surface of a sheet of glass, and since one cannot predict where a gaseous inclusion will end up relative to the surface of a sheet, gaseous inclusions must be avoided at all cost. Furthermore, for processing simplicity, TFT manufacturers often seek to have color filter glass made from the same substrate material used in the TFT manufacturing process, in which case gaseous inclusions can block pixels, thereby compromising performance of the entire device. To clear gaseous defects from the glass melt before it is made into sheet, it is conventional to add fining agents Fining agents are multivalent cations or halides that release gas at high temperature. Exemplary multivalent fining agents include, but are not limited to, As 2 O 3 , Sb 2 O 3 , SnO 2 , and Fe 2 O 3 . Waste streams containing arsenic and antimony are considered hazardous materials in some countries, and for this reason is may be desirable to limit their concentrations in the inventive glass. In a preferred embodiment of the inventive glasses, As 2 O 3 , Sb 2 O 3 , or combinations thereof are kept at a level of 500 ppm (0.05 wt %) or less. 
         [0036]    Halogens that find use as fining agents include F, Cl and Br. Waste streams that contain halogens may also be regarded as hazardous materials in some countries, and their release during melting processes can cause excessive corrosion of steel ductwork and supports. On the other hand, melt systems can be designed to safely handle off-gas of halogens, and various choices of raw materials can be used to influence their retention in the final glass. Halogens are typically added as stable salts, which may include, but are not limited to, simple salts and hydrated salts of the alkaline earths or aluminum, such as MgF 2 , CaF 2 , SrF 2 , BaF 2 , MgCl 2 , CaCl 2 , SrCl 2 , BaCl 2 , MgCl 2 .4H 2 O, CaCl 2 .4H 2 O, SrCl 2 .4H 2 O, BaCl 2 .4H 2 O, MgBr 2 , CaBr 2 , SrBr 2 , BaBr 2 , MgBr 2 .4H 2 O, CaBr 2 .4H 2 O, SrBr 2 .4H 2 O, BaBr 2 .4H 2 O, AlCl 3 , AlCl 3 .6H 2 O, and other forms familiar to those skilled in the art of raw material selection Fining is generally optimized at a relatively low level of halogen addition, and thus the inventive glasses have F+Cl+Br concentrations between 0 and 0.4 mol %. In a preferred embodiment, F+Cl+Br is less than 200 ppm, or 0.02 wt %. 
         [0037]      FIG. 1  demonstrates a comparison of a glass typical of this invention (X) with typical p-Si glasses. Compaction is measured relative to a base composition  1  in both an internal compaction measurement and in a display manufacturing cycle, where 50% of 11s considered an acceptable level of compaction and less than 25% of 11s preferable. Glasses  1 ,  2 , and  3  have been put through the display manufacturing process as well as our the inventor&#39;s simulated internal tests and are included to demonstrate the transparency of the internal simulation with actual display maker&#39;s feedback. Glass  4  is Corning&#39;s Jade® composition and Glass  5  is a typical annealed p-Si composition, both showing acceptable levels of compaction. Glass  6  is a “more annealed” p-Si glass demonstrating lower compaction relative to the “typical” Glass  5 . It is clear that the glasses in this invention (typified by glass X) have comparable, if not superior, compaction performance than either annealed p-Si glass and clearly superior compaction relative to Jade®. 
         [0038]      FIG. 2  demonstrates thermal sag (measured as “Deflection” in the y-axis) at 700° C. of typical p-Si glasses (Glass  6  and Jade®) relative to glasses typical of this invention (“X”). It is clear the X glass has superior sag behavior at 700° C. than either other p-Si glass, thereby enabling higher temperature thermal cycles for use in a display manufacturer&#39;s process. 
         [0039]      FIG. 3  demonstrates an interesting relationship that was observed with respect to the ratio of the SiO 2 +Al 2 O 3  content to 1-B 2 O 3  content and the RO—Al 2 O 3  content. Many of the advantageous compositions of the present invention were located on the line y=0.7132x+86.965, as demonstrated graphically in  FIG. 3 . Put another way, in one embodiment, the glasses of the present invention fall within the following relationship: SiO 2 +Al 2 O 3 =86.97−0.713*(MgO+CaO+SrO+BaO—Al 2 O 3 )±0.8. 
       EXAMPLES 
       [0040]    The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention which are apparent to one skilled in the art. 
         [0041]    Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in ° C. or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of reaction conditions, e.g., component concentrations, temperatures, pressures and other reaction ranges and conditions that can be used to optimize the product purity and yield obtained from the described process. Only reasonable and routine experimentation will be required to optimize such process conditions. 
         [0042]    Table 1 shows an example of an exemplary inventive glass composition based from to Example 16 in Table 2, and a particular selection of raw materials for making it. As is known to those skilled in the art of glass manufacture, the particular choice of raw materials does not impact the final glass composition as the original raw materials are transformed into a single, uniform glass by the melting process. However, the actual choice of raw materials may be different than indicated in light of the particular requirements imposed by the limitations of a particular melting system, or by the cost of the raw materials, or both. 
         [0043]    The primary source of SiO 2  is sand. The sand can be obtained from one or more of a variety of sources, including sand deposits (beaches or dunes), sandstone, quartzite, or other sources known to those skilled in the art of raw material selection. Sand is often the primary source of alkali contamination in what would otherwise be alkali-free glasses, and therefore a careful selection of source material may be important to minimize this important contaminant. The size of the sand particles may influence the rate of melting, and in particular large sand grains may fail to melt completely, appearing in the wear as a knot or stone. To avoid this, it is generally preferable for more than 90% of all sand grains to pass through a standard #80 U.S. standard mesh size. Alumina itself is generally the least expensive raw material to add Al 2 O 3  to a glass, but other materials such as the aluminosilicate kaolin or hydrous forms of alumina or polymorphs of Al 2 O 3  can be used instead when raw material costs are less important. 
         [0044]    While Example 16 does not intentionally contain B 2 O 3 , other examples do. B 2 O 3  can be batched as boric anhydride (approximately 94+% B 2 O 3 , the balance being mostly H 2 O) or boric acid, approximately B(OH) 3 . 
         [0045]    MgO is generally added as its oxide, while the other alkaline earths are typically batched as carbonates. Suitable carbonate sources for CaO include limestone and precipitated calcium carbonate (a refined limestone product). MgO can be batched with CaO in the form of dolomite, though this may also increase the amount of iron in the glass, and so may be undesirable as compared to a more predictable pure iron source. Most of the strontium and barium will generally be added as carbonates obtained by industrial chemical processes. However, to keep the batch adequately oxidized, it is generally desirable to include a nitrate source as well. Strontium nitrate is indicated in the batch, but barium nitrate will work just as well. In both cases, it is generally desirable to batch no more than about 1 mol % of the alkaline earth oxide as nitrates to reduce NO x  emissions, but in other ways nitrates may assist melting, so the exact amount that will work best is generally the subject of trial-and-error investigation. 
         [0046]    SnO 2  is included in its usual role as a fining agent. More SnO 2  generally equates to improved fining capacity, but as it is a comparatively expensive raw material, it is desirable to add no more than is required to drive gaseous inclusions to an appropriately low level. The SnO 2  level of the inventive glass is preferably between 0.02 and 0.3 mol %. 
         [0047]    A low amount of ZrO 2  (zirconia) is included in this example. It serves no practical role in the melting or fining behavior of the glass, and imparts no interesting properties at such a low level. It is useful to include it in a laboratory-scale batch, however, because it will be introduced by contact of hot glass with zirconia-based refractory materials in the melter, and thus monitoring its level in the glass may be important to judging the rate of tank wear over time. A typical amount of ZrO in the final glass of one embodiment is less than 0.05 mol %. In another embodiment, the amount of ZrO is less than 500 ppm. 
         [0048]    The batch shows a low level of iron. Some iron is all but unavoidable due to contamination introduced by raw materials, especially sand and typical sources of MgO. Iron may also be added to benefit fining, hydrogen permeation, or both. If deliberately added, iron oxalate is a particularly useful raw material, but other compounds of iron can be employed as well. Iron can impart color to the glass if it becomes too oxidized, and so the level of iron is preferably between 0.01 and 0.08 mol % to obtain the best balance between gaseous inclusion management and excessive color. 
         [0049]    A significant amount of water accompanies boric acid and sand, and a significant amount of carbon dioxide accompanies the carbonate raw materials. CO 2  is sparingly soluble in glass, so most of it is lost in the earliest stages of melting, and that which is trapped in gaseous inclusions is generally moved by action of the fining agent, e.g., SnO 2  in the present example. A significant level of water may be retained in the glass, however, in the form of dissolved OH −  ions. This results in a measurable OH −  vibrational band near 3600 cm −1  in the near infrared. The intensity of this band above background through a 1 mm thick path length is referred to as β OH . It generally ranges from as low as 0.2 to as high as 0.7 in conventional amorphous silicon substrate glasses. Dissolved OH −  has a large impact on the annealing point for alkali-free glasses, and therefore it is desirable to keep OH −  as low as reasonably achievable for any given glass. Conventional electric-boost melters generally employ burners above the glass surface that generate a high water partial pressure and result in higher levels of water incorporation into the glass. Halides can be used to reduce the retained water level, and boosting the power delivered via electrodes and reducing the power delivered via burners can also help. Likewise, selecting a comparatively dry sand can produce enough of a change in dissolved OH −  to significantly impact annealing point. β OH  for the inventive glass is less than 0.55, in one embodiment, less than 0.5 in another embodiment, and less than 0.45 in yet another embodiment to maximize the annealing point of the final glass. 
         [0050]    While the actual composition and the choice of raw materials in this example is quite specific, it will be obvious to one skilled in the art that alternative raw materials can be used to obtain the same final glass composition, and thus a particular set of raw materials must be selected so as to be best suited for a given melting/fining/forming process. Any other set of raw materials that results in an equivalent composition will therefore produce a glass that satisfies the basic requirement of high annealing point, low density, low CTE, and high durability required for low-temperature polysilicon applications. 
         [0051]    Further and although the intended use for the disclosed glasses is in p-Si applications, it should be noted that the glasses may also be considered for a-Si, color filter substrate or other applications where the disclosed properties may be deemed advantageous. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 mol % 
                 batch weight (g) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 SiO 2   
                 sand 
                 71.86 
                 596.99 
               
               
                 Al 2 O 3   
                 alumina 
                 11.72 
                 174.35 
               
               
                 MgO 
                 magnesia 
                 5.17 
                 30.36 
               
               
                 CaO 
                 limestone 
                 5.59 
                 84.65 
               
               
                 SrO 
                 strontium carbonate 
                 1.42 
                 28.45 
               
               
                 BaO 
                 barium carbonate 
                 4.05 
                 119.78 
               
               
                 SnO 2   
                 tin (IV) oxide, 10% C.B. 
                 0.15 
                 33 
               
               
                 Fe 2 O 3   
                 iron oxalate 10% C.B. 
                 0.02 
                 5.349 
               
               
                 ZrO 2   
                 zirconium oxide 20% C.B. 
                 0.02 
                 2.02 
               
               
                   
               
             
          
         
       
     
       Example 
     Preparation of a Test Sample 
       [0052]    TABLE 2 sets forth exemplary glass compositions in mol percent, as calculated on an oxide basis from the glass batches. These example glasses were prepared by melting 1,000-25,000 gram batches of each glass composition at a temperature and time to result in a relatively homogeneous glass composition, e.g. at a temperature of about 1625° C. for a period of about 4-16 hours in platinum crucibles. Also set forth are relevant glass properties for each glass composition, determined on the glasses in accordance with techniques conventional in the glass art. Thus, the linear coefficient of thermal expansion (CTE) over the temperature range 0-300° C. is expressed in terms of ×10 −7 /° C., the softening point (Soft. Pt.), and the annealing point (Ann. Pt.), and strain point (Str. Pt.) are expressed in terms of ° C. These were determined from fiber elongation techniques (ASTM references E228-85, C338, and C336, respectively). The density (Den.), in terms of g/cm 3 , was measured via the Archimedes method (ASTM C693). 
         [0053]    The 200 poise temperature (Melt. Temp., ° C.) (defined as the temperature at which the glass melt demonstrates a viscosity of 200 poises [20 Pa·s]) was calculated employing the Fulcher equation fit to the high temperature viscosity data (measure via rotating cylinders viscometry, ASTM C965-81). The liquidus temperature (Liq. Temp.) of the glass was measured using the standard liquidus method. This involves placing crushed glass particles in a platinum boat, placing the boat in a furnace having a region of gradient temperatures, heating the boat in an appropriate temperature region for 24 hours, and determining by means of microscopic examination the highest temperature at which crystals appear in the interior of the glass. The liquidus viscosity (Liq. Visc., in poises) was determined from this temperature and the coefficients of the Fulcher equation. 
         [0054]    The remainder of properties listed in Table 2 are achieved through standard tests that are well known to those of skill in the industry. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 Example 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 70.75 
                 72.33 
                 72.19 
                 71.68 
                 73.11 
                 71.75 
               
               
                   
                 A l2 O 3   
                 11.96 
                 11.85 
                 11.36 
                 11.46 
                 11.6 
                 12.17 
               
               
                   
                 B 2 O 3   
                 1.23 
                 0 
                 1.55 
                 1.6 
                 0 
                 0 
               
               
                   
                 MgO 
                 5.88 
                 4.92 
                 4.73 
                 4.44 
                 4.81 
                 5.93 
               
               
                   
                 CaO 
                 5.3 
                 5.16 
                 5.22 
                 5.37 
                 5.19 
                 5.28 
               
               
                   
                 SrO 
                 2.04 
                 3.11 
                 1.87 
                 2.44 
                 1.35 
                 2.1 
               
               
                   
                 BaO 
                 2.68 
                 2.46 
                 2.95 
                 2.81 
                 3.81 
                 2.61 
               
               
                   
                 SnO 2   
                 0.11 
                 0.12 
                 0.12 
                 0.15 
                 0.12 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.01 
                 0.02 
                 0.01 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0 
                 0.02 
                 0 
                 0.03 
               
               
                   
                 RO/Al 2 O 3   
                 1.33 
                 1.32 
                 1.3 
                 1.31 
                 1.31 
                 1.31 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.99 
                 3.8 
                 3.46 
                 3.66 
                 3.56 
                 3.75 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.74 
                 84.18 
                 84.87 
                 84.49 
                 84.71 
                 83.92 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.37 
                 0.31 
                 0.32 
                 0.29 
                 0.32 
                 0.37 
               
               
                 Properties 
                 Strain 
                 740 
                 761 
                 742 
                 740 
                 765 
                 764 
               
               
                   
                 Anneal 
                 793 
                 818 
                 797 
                 794 
                 820 
                 817 
               
               
                   
                 Soft (ppv) 
                 1030.1 
                 1059.5 
                 1043.6 
                 1042.5 
                   
                 1052.8 
               
               
                   
                 CTE (disk) 
                 36.2 
                 36.1 
                 35.6 
                 35.3 
                 36.7 
                 35.9 
               
               
                   
                 Density 
                 2.595 
                 2.604 
                 2.575 
                 2.586 
                 2.611 
                 2.601 
               
               
                   
                 Young&#39;s modulus 
                 12.178 
                 12.187 
                 11.904 
                 11.92 
                 12.076 
                 12.371 
               
               
                   
                 specific modulus 
                 32.4 
                 32.3 
                 31.9 
                 31.8 
                 31.9 
                 32.8 
               
               
                 Viscosity 
                 A 
                 −3.039 
                 −3.318 
                 −3.089 
                 −2.936 
                 −3.179 
                 −2.77 
               
               
                   
                 B 
                 6851.7 
                 7509.3 
                 7314.4 
                 6813.9 
                 7321.7 
                 6440.1 
               
               
                   
                 To 
                 380.6 
                 364.2 
                 347 
                 391.5 
                 376.7 
                 423.8 
               
               
                   
                 200 poise 
                 1664 
                 1701 
                 1704 
                 1693 
                 1713 
                 1694 
               
               
                   
                 400 poise 
                 1595 
                 1633 
                 1632 
                 1622 
                 1643 
                 1623 
               
               
                   
                 35000 poise 
                 1284 
                 1319 
                 1305 
                 1302 
                 1325 
                 1304 
               
               
                 Gradient boat 
                 internal 
                 1210 
                 1240 
                 1225 
                 1210 
                 1250 
                 1220 
               
               
                   
                 internal viscosity 
                 166737 
                 180392.2 
                 174482.4 
                 244828.8 
                 160304.6 
                 208231.1 
               
               
                   
                 T(35 kp) − T(liq) 
                 74 
                 79 
                 80 
                 92 
                 75 
                 84 
               
               
                   
               
             
          
           
               
                 Example 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
               
               
                   
               
             
          
           
               
                 mol % 
                 SiO 2   
                 71.99 
                 71.21 
                 72.48 
                 71.79 
                 71.33 
                 71.33 
                 73.59 
               
               
                   
                 Al 2 O 3   
                 11.59 
                 11.59 
                 11.73 
                 12.61 
                 11.49 
                 11.58 
                 11.37 
               
               
                   
                 B 2 O 3   
                 0 
                 1.19 
                 0 
                 1.72 
                 1.29 
                 1.53 
                 0 
               
               
                   
                 MgO 
                 5.51 
                 5.32 
                 4.95 
                 3.94 
                 5.21 
                 4.65 
                 4.73 
               
               
                   
                 CaO 
                 5.41 
                 5.36 
                 5.53 
                 5.03 
                 5.33 
                 5.79 
                 5.11 
               
               
                   
                 SrO 
                 1.18 
                 1.4 
                 1.82 
                 1.21 
                 1.28 
                 1.69 
                 1.32 
               
               
                   
                 BaO 
                 4.16 
                 3.78 
                 3.31 
                 3.54 
                 3.91 
                 3.24 
                 3.74 
               
               
                   
                 SnO 2   
                 0.11 
                 0.11 
                 0.14 
                 0.12 
                 0.11 
                 0.15 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.03 
                 0.02 
                 0.02 
                 0.01 
                 0.02 
                 0.02 
                 0.01 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0 
               
               
                   
                 RO/Al 2 O 3   
                 1.4 
                 1.37 
                 1.33 
                 1.09 
                 1.37 
                 1.33 
                 1.31 
               
               
                   
                 (RO − Al 2 O 3 )/ 
                 4.67 
                 4.32 
                 3.88 
                 1.13 
                 4.3 
                 3.85 
                 3.53 
               
               
                   
                 (1 − B 2 O 3 /100) 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/ 
                 83.58 
                 83.8 
                 84.21 
                 85.88 
                 83.9 
                 84.2 
                 84.96 
               
               
                   
                 (1 − B 2 O 3 /100) 
               
               
                   
                 MgO/(MgO + 
                 0.34 
                 0.34 
                 0.32 
                 0.29 
                 0.33 
                 0.3 
                 0.32 
               
               
                   
                 CaO + SrO + BaO) 
               
               
                 Proper- 
                 Strain 
                 759 
                 744 
                 764 
                 752 
                 745 
                 738 
                 765 
               
               
                 ties 
                 Anneal 
                 813 
                 797 
                 818 
                 806 
                 798 
                 794 
                 821 
               
               
                   
                 Soft (ppv) 
                 1052.3 
                 1038.6 
                 1058 
                   
                 1035.1 
                 1037.3 
                 1073.1 
               
               
                   
                 CTE (disk) 
                 36.4 
                 36.5 
                   
                 35.5 
                 33.8 
                 36.8 
                 35.9 
               
               
                   
                 Density 
                 2.629 
                 2.612 
                 2.611 
                   
                 2.612 
                 2.594 
                 2.592 
               
               
                   
                 Young&#39;s 
                 12.12 
                 12.083 
                 12.086 
                   
                 12.003 
                 11.932 
                 12.011 
               
               
                   
                 modulus 
               
               
                   
                 specific 
                 31.8 
                 31.9 
                 31.9 
                   
                 31.7 
                 31.7 
                 31.9 
               
               
                   
                 modulus 
               
               
                 Vis- 
                 A 
                 −3.281 
                 −3.058 
                 −2.963 
                 −2.9388 
                 −3.267 
                 −3.416 
                 −3.229 
               
               
                 cosity 
                 B 
                 7682.3 
                 7027.4 
                 6997.2 
                 6854.51 
                 7471.1 
                 7756.7 
                 7499 
               
               
                   
                 To 
                 329.9 
                 369.3 
                 384.4 
                 397.06 
                 338.2 
                 326.9 
                 368.2 
               
               
                   
                 200 poise 
                 1706 
                 1681 
                 1714 
                 1705 
                 1680 
                 1684 
                 1724 
               
               
                   
                 400 poise 
                 1636 
                 1611 
                 1642 
                 1634 
                 1611 
                 1616 
                 1654 
               
               
                   
                 35000 poise 
                 1312 
                 1294 
                 1316 
                 1313 
                 1295 
                 1301 
                 1333 
               
               
                 Gradient 
                 internal 
                 1220 
                 1190 
                 1205 
                 1185 
                 1185 
                 1200 
                 1250 
               
               
                 boat 
                 internal 
                 223783.5 
                 319661.5 
                 366379.8 
                 576075.1 
                 359537.7 
                 293826.6 
                 188449 
               
               
                   
                 viscosity 
               
               
                   
                 T(35 kp) − 
                 92 
                 104 
                 111 
                 128 
                 110 
                 101 
                 83 
               
               
                   
                 T(liq) 
               
               
                   
               
             
          
           
               
                 Example 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.27 
                 73.26 
                 71.86 
                 72.08 
                 72.09 
                 72.78 
               
               
                   
                 Al 2 O 3   
                 11.9 
                 11.09 
                 11.72 
                 11.76 
                 12.05 
                 11.39 
               
               
                   
                 B 2 O 3   
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 MgO 
                 4.92 
                 4.61 
                 5.17 
                 5.34 
                 5.4 
                 4.91 
               
               
                   
                 CaO 
                 6.16 
                 4.98 
                 5.59 
                 5.44 
                 5.38 
                 5.44 
               
               
                   
                 SrO 
                 2.13 
                 1.29 
                 1.42 
                 1.6 
                 2.03 
                 1.68 
               
               
                   
                 BaO 
                 2.46 
                 3.63 
                 4.05 
                 3.62 
                 2.93 
                 3.65 
               
               
                   
                 SnO 2   
                 0.12 
                 0.12 
                 0.15 
                 0.11 
                 0.1 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.01 
                 0.02 
                 0.02 
                 0.01 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.32 
                 1.31 
                 1.38 
                 1.36 
                 1.31 
                 1.38 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.77 
                 3.45 
                 4.51 
                 4.24 
                 3.69 
                 4.29 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.17 
                 85.2 
                 83.58 
                 83.84 
                 84.14 
                 84.17 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.31 
                 0.32 
                 0.32 
                 0.33 
                 0.34 
                 0.31 
               
               
                 Properties 
                 Strain 
                 765 
                 749 
                 760 
                 759 
                 762 
                 762 
               
               
                   
                 Anneal 
                 818 
                 806 
                 814 
                 813 
                 816 
                 815 
               
               
                   
                 Soft (ppv) 
                 1055.3 
                 1059.6 
                 1052.2 
                 1051.4 
                 1050 
                 1056.8 
               
               
                   
                 CTE (disk) 
                 35.9 
                 35.8 
                 37.3 
                 36.1 
                 37.1 
                 37.2 
               
               
                   
                 Density 
                 2.591 
                 2.572 
                 2.632 
                 2.619 
                 2.603 
                 2.616 
               
               
                   
                 Young&#39;s modulus 
                 12.228 
                 11.769 
                   
                 12.158 
               
               
                   
                 specific modulus 
                 32.5 
                 31.5 
                 0 
                 32 
                   
                 0 
               
               
                 Viscosity 
                 A 
                 −3.143 
                 −3.447 
                 −3.156 
                 −3.201 
                 −3.227 
                 −2.954 
               
               
                   
                 B 
                 7180.4 
                 8201 
                 7237.7 
                 7221.9 
                 7345.25 
                 7021.4 
               
               
                   
                 To 
                 381.1 
                 290.5 
                 370.5 
                 379.5 
                 368.95 
                 385.6 
               
               
                   
                 200 poise 
                 1700 
                 1717 
                 1697 
                 1692 
                 1698 
                 1722 
               
               
                   
                 400 poise 
                 1631 
                 1646 
                 1627 
                 1624 
                 1629 
                 1649 
               
               
                   
                 35000 poise 
                 1315 
                 1317 
                 1310 
                 1312 
                 1314 
                 1322 
               
               
                 Gradient boat 
                 internal 
                 1240 
                 1245 
                 1195 
                 1200 
                 1225 
                 1230 
               
               
                   
                 internal viscosity 
                 164814.5 
                 139615.3 
                 419073.2 
                 398867 
                 225630.8 
                 229748.9 
               
               
                   
                 T(35 kp) − T(liq) 
                 75 
                 72 
                 115 
                 112 
                 89 
                 92 
               
               
                   
               
             
          
           
               
                 Example 
                 20 
                 21 
                 22 
                 23 
                 24 
                 25 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.19 
                 71.45 
                 73.18 
                 72.39 
                 72.65 
                 71.59 
               
               
                   
                 Al 2 O 3   
                 12.2 
                 12.05 
                 11.95 
                 11.74 
                 11.72 
                 11.73 
               
               
                   
                 B 2 O 3   
                 1 
                 1.25 
                 0.5 
                 0 
                 0 
                 1.65 
               
               
                   
                 MgO 
                 4.61 
                 4.9 
                 4.56 
                 5.14 
                 4.86 
                 4.75 
               
               
                   
                 CaO 
                 4.9 
                 5.5 
                 4.88 
                 5.34 
                 5.59 
                 5.5 
               
               
                   
                 SrO 
                 1.3 
                 1.55 
                 1.24 
                 1.22 
                 2.58 
                 2 
               
               
                   
                 BaO 
                 3.6 
                 3.15 
                 3.54 
                 4.02 
                 2.43 
                 2.65 
               
               
                   
                 SnO 2   
                 0.16 
                 0.12 
                 0.13 
                 0.11 
                 0.12 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.03 
                 0.02 
                 0.01 
                 0.02 
                 0.01 
               
               
                   
                 ZrO 2   
                 0.02 
                 0 
                 0 
                 0.02 
                 0.03 
                 0 
               
               
                   
                 RO/Al 2 O 3   
                 1.18 
                 1.25 
                 1.19 
                 1.34 
                 1.32 
                 1.27 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 2.23 
                 3.09 
                 2.28 
                 3.98 
                 3.74 
                 3.22 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 85.24 
                 84.56 
                 85.56 
                 84.13 
                 84.37 
                 84.72 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.32 
                 0.32 
                 0.33 
                 0.31 
                 0.32 
               
               
                 Properties 
                 Strain 
                 752 
                 738 
                 767 
                 761 
                 765 
                 743 
               
               
                   
                 Anneal 
                 807 
                 793 
                 821 
                 817 
                 819 
                 797 
               
               
                   
                 Soft (ppv) 
                 1050.2 
                 1034.2 
                 1069.5 
                 1060.2 
                 1058.6 
                 1039.8 
               
               
                   
                 CTE (disk) 
                 35.4 
                 36.2 
                 34.4 
                 34 
                 36.4 
                 35.9 
               
               
                   
                 Density 
                 2.603 
                 2.603 
                 2.577 
                 2.62 
                 2.594 
                 2.574 
               
               
                   
                 Young&#39;s modulus 
                   
                 12.112 
                 11.951 
                 12.115 
                 12.163 
                 11.929 
               
               
                   
                 specific modulus 
                 0 
                 32.1 
                 32 
                 31.9 
                 32.3 
                 32 
               
               
                 Viscosity 
                 A 
                 −3.232 
                 −2.868 
                 −3.354 
                 −3.061 
                 −2.77 
                 −3.044 
               
               
                   
                 B 
                 7311.1 
                 6597.4 
                 7841.5 
                 7095.3 
                 6633.3 
                 7080.4 
               
               
                   
                 To 
                 370.6 
                 398 
                 326.5 
                 388.7 
                 408.9 
                 365.7 
               
               
                   
                 200 poise 
                 1692 
                 1674 
                 1713 
                 1712 
                 1717 
                 1690 
               
               
                   
                 400 poise 
                 1624 
                 1604 
                 1643 
                 1642 
                 1644 
                 1620 
               
               
                   
                 35000 poise 
                 1311 
                 1288 
                 1319 
                 1322 
                 1316 
                 1299 
               
               
                 Gradient boat 
                 internal 
                 1220 
                 1205 
                 1230 
                 1225 
                 1240 
                 1220 
               
               
                   
                 internal viscosity 
                 237339.4 
                 202869.5 
                 211361.6 
                 264945.4 
                 162685.9 
                 175369.9 
               
               
                   
                 T(35 kp) − T(liq) 
                 91 
                 83 
                 89 
                 97 
                 76 
                 79 
               
               
                   
               
             
          
           
               
                 Example 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.71 
                 72.7 
                 72.21 
                 71.14 
                 72.85 
                 71.97 
               
               
                   
                 Al 2 O 3   
                 11.24 
                 11.38 
                 11.62 
                 11.27 
                 11.37 
                 12.02 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 0 
                 0.91 
                 0 
                 0 
               
               
                   
                 MgO 
                 5.95 
                 3.88 
                 5.24 
                 5.68 
                 4.85 
                 4.98 
               
               
                   
                 CaO 
                 5.5 
                 5.74 
                 5.47 
                 5.46 
                 5.73 
                 6.23 
               
               
                   
                 SrO 
                 1.03 
                 2.83 
                 1.2 
                 1.1 
                 0.92 
                 2.15 
               
               
                   
                 BaO 
                 4.38 
                 3.31 
                 4.09 
                 4.27 
                 4.13 
                 2.49 
               
               
                   
                 SnO 2   
                 0.11 
                 0.11 
                 0.11 
                 0.11 
                 0.11 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.05 
                 0.02 
                 0.02 
                 0.04 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.03 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.03 
               
               
                   
                 RO/Al 2 O 3   
                 1.5 
                 1.38 
                 1.38 
                 1.46 
                 1.37 
                 1.32 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 5.62 
                 4.38 
                 4.38 
                 5.29 
                 4.26 
                 3.83 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 82.95 
                 84.08 
                 83.83 
                 83.17 
                 84.22 
                 83.99 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.35 
                 0.25 
                 0.33 
                 0.34 
                 0.31 
                 0.31 
               
               
                 Properties 
                 Strain 
                 755 
                 761 
                 764 
                 740 
                 760 
                 766 
               
               
                   
                 Anneal 
                 807 
                 816 
                 816 
                 793 
                 814 
                 819 
               
               
                   
                 Soft (ppv) 
                 1043 
                 1056.7 
                 1047.7 
                 1033.1 
                 1058.9 
                 1056 
               
               
                   
                 CTE (disk) 
                   
                 38.2 
                   
                 37 
                 36.2 
               
               
                   
                 Density 
                 2.637 
                 2.627 
                 2.625 
                 2.629 
                 2.618 
                 2.593 
               
               
                   
                 Young&#39;s modulus 
                 12.099 
                 12.052 
                 12.062 
                 11.947 
                 12.006 
                 12.299 
               
               
                   
                 specific modulus 
                 31.6 
                 31.6 
                 31.7 
                 31.3 
                 31.6 
                 32.7 
               
               
                 Viscosity 
                 A 
                 −2.927 
                 −3.158 
                 −3.245 
                 −3 
                 −2.577 
                 −3.031 
               
               
                   
                 B 
                 6767.8 
                 7404.8 
                 7464.1 
                 6922.1 
                 6367.7 
                 7014.5 
               
               
                   
                 To 
                 400.7 
                 361.3 
                 354.3 
                 371.5 
                 425.3 
                 383.8 
               
               
                   
                 200 poise 
                 1695 
                 1718 
                 1700 
                 1677 
                 1731 
                 1699 
               
               
                   
                 400 poise 
                 1625 
                 1647 
                 1631 
                 1607 
                 1655 
                 1629 
               
               
                   
                 35000 poise 
                 1307 
                 1323 
                 1313 
                 1289 
                 1320 
                 1310 
               
               
                 Gradient boat 
                 internal 
                 1200 
                 1230 
                 1200 
                 1190 
                 1210 
                 1235 
               
               
                   
                 internal viscosity 
                 346863.6 
                 232274.4 
                 381015.8 
                 286454.5 
                 345001.5 
                 162076.1 
               
               
                   
                 T(35 kp) − T(liq) 
                 107 
                 93 
                 113 
                 99 
                 110 
                 75 
               
               
                   
               
             
          
           
               
                 Example 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.66 
                 70.82 
                 72 
                 74.05 
                 72.8 
                 72.83 
               
               
                   
                 Al 2 O 3   
                 12.19 
                 12.07 
                 11.65 
                 12.03 
                 11.37 
                 11.38 
               
               
                   
                 B 2 O 3   
                 0 
                 1 
                 1.65 
                 0 
                 0 
                 0 
               
               
                   
                 MgO 
                 6.22 
                 6.01 
                 4.75 
                 4.34 
                 4.29 
                 5.38 
               
               
                   
                 CaO 
                 5.33 
                 5.27 
                 5.3 
                 4.73 
                 5.72 
                 5.19 
               
               
                   
                 SrO 
                 2.25 
                 2.16 
                 1.5 
                 1.18 
                 2.08 
                 0.88 
               
               
                   
                 BaO 
                 2.18 
                 2.5 
                 3 
                 3.53 
                 3.57 
                 4.19 
               
               
                   
                 SnO 2   
                 0.12 
                 0.12 
                 0.12 
                 0.11 
                 0.11 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.03 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.03 
                 0 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.31 
                 1.32 
                 1.25 
                 1.15 
                 1.38 
                 1.37 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.79 
                 3.91 
                 2.95 
                 1.75 
                 4.29 
                 4.26 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.85 
                 83.73 
                 85.05 
                 86.08 
                 84.17 
                 84.21 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.39 
                 0.38 
                 0.33 
                 0.31 
                 0.27 
                 0.34 
               
               
                 Properties 
                 Strain 
                 764 
                 745 
                 740 
                 774 
                 760 
                 761 
               
               
                   
                 Anneal 
                 816 
                 799 
                 794 
                 830 
                 814 
                 815 
               
               
                   
                 Soft (ppv) 
                 1049.4 
                 1034 
                 1034.9 
                 1079 
                 1057.4 
                 1056.4 
               
               
                   
                 CTE (disk) 
                 35.9 
                 37 
                 34.8 
                 34.3 
                 36.8 
                 36.9 
               
               
                   
                 Density 
                 2.591 
                 2.59 
                 2.582 
                 2.58 
                 2.622 
                 2.621 
               
               
                   
                 Young&#39;s modulus 
                 12.402 
                   
                 11.99 
                 11.981 
                   
                 12.113 
               
               
                   
                 specific modulus 
                 33 
                   
                 32 
                 32 
                 0 
                 31.9 
               
               
                 Viscosity 
                 A 
                 −3.426 
                 −3.2055 
                 −2.778 
                 −2.998 
                 −3.145 
                 −2.35 
               
               
                   
                 B 
                 7613.4 
                 7086.72 
                 6477.2 
                 7183 
                 7387 
                 5942.8 
               
               
                   
                 To 
                 344.8 
                 377.78 
                 407.6 
                 390.8 
                 360.1 
                 455.9 
               
               
                   
                 200 poise 
                 1674 
                 1665 
                 1683 
                 1746 
                 1717 
                 1734 
               
               
                   
                 400 poise 
                 1608 
                 1598 
                 1612 
                 1673 
                 1645 
                 1656 
               
               
                   
                 35000 poise 
                 1300 
                 1292 
                 1292 
                 1343 
                 1321 
                 1318 
               
               
                 Gradient boat 
                 internal 
                 1230 
                 1215 
                 1200 
                 1245 
                 1210 
                 1215 
               
               
                   
                 internal viscosity 
                 149543.7 
                 181587.2 
                 248974.3 
                 257654.5 
                 352055.2 
                 301123.4 
               
               
                   
                 T(35 kp) − T(liq) 
                 70 
                 77 
                 92 
                 98 
                 111 
                 103 
               
               
                   
               
             
          
           
               
                 Example 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.6 
                 72.61 
                 72.31 
                 71.69 
                 72.31 
                 71.27 
               
               
                   
                 Al 2 O 3   
                 11.81 
                 11.81 
                 11.59 
                 11.88 
                 12.04 
                 12.27 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 1.72 
               
               
                   
                 MgO 
                 5.54 
                 4.91 
                 4.82 
                 5.97 
                 4.88 
                 4.2 
               
               
                   
                 CaO 
                 5.49 
                 5.3 
                 5.95 
                 5.39 
                 5.38 
                 5.34 
               
               
                   
                 SrO 
                 1.23 
                 1.37 
                 0.99 
                 1.93 
                 1.39 
                 1.29 
               
               
                   
                 BaO 
                 4.19 
                 3.88 
                 4.18 
                 2.99 
                 3.87 
                 3.76 
               
               
                   
                 SnO 2   
                 0.11 
                 0.12 
                 0.11 
                 0.11 
                 0.11 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.01 
                 0.02 
                 0.02 
                 0.01 
                 0.01 
               
               
                   
                 ZrO 2   
                 0.02 
                 0 
                 0.02 
                 0.02 
                 0 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.39 
                 1.31 
                 1.38 
                 1.37 
                 1.29 
                 1.19 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 4.64 
                 3.65 
                 4.35 
                 4.4 
                 3.48 
                 2.36 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.41 
                 84.42 
                 83.9 
                 83.57 
                 84.35 
                 85 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.34 
                 0.32 
                 0.3 
                 0.37 
                 0.31 
                 0.29 
               
               
                 Properties 
                 Strain 
                 759 
                 765 
                 759 
                 762 
                 764 
                 741 
               
               
                   
                 Anneal 
                 811 
                 819 
                 813 
                 814 
                 818 
                 794 
               
               
                   
                 Soft (ppv) 
                 1049.2 
                 1059.3 
                 1055.6 
                 1050.6 
               
               
                   
                 CTE (disk) 
                 37.9 
                 36.7 
                 36.7 
                 36.5 
                   
                 36.7 
               
               
                   
                 Density 
                 2.632 
                 2.624 
                 2.627 
                 2.612 
                 2.617 
               
               
                   
                 Young&#39;s modulus 
                 12.231 
                 12.096 
                 12.124 
                 12.343 
                 12.049 
               
               
                   
                 specific modulus 
                 32 
                 31.8 
                 31.8 
                 32.6 
                 31.7 
               
               
                 Viscosity 
                 A 
                 −3.603 
                 −3.326 
                 −3.147 
                 −3.062 
                 −2.976 
                 −2.8813 
               
               
                   
                 B 
                 8091.9 
                 7540.6 
                 7223.2 
                 6951.8 
                 7088.4 
                 6732.21 
               
               
                   
                 To 
                 319.2 
                 361.5 
                 376.4 
                 388.2 
                 371.8 
                 389.92 
               
               
                   
                 200 poise 
                 1690 
                 1702 
                 1702 
                 1684 
                 1715 
                 1689 
               
               
                   
                 400 poise 
                 1623 
                 1634 
                 1633 
                 1616 
                 1643 
                 1618 
               
               
                   
                 35000 poise 
                 1312 
                 1320 
                 1316 
                 1302 
                 1314 
                 1297 
               
               
                 Gradient boat 
                 internal 
                 1220 
                 1250 
                 1200 
                 1220 
                 1200 
                 1185 
               
               
                   
                 internal viscosity 
                 239891.6 
                 144839.8 
                 420026.6 
                 197486.7 
                 382650.4 
                 385510.9 
               
               
                   
                 T(35 kp) − T(liq) 
                 92 
                 70 
                 116 
                 82 
                 114 
                 112 
               
               
                   
               
             
          
           
               
                 Example 
                 44 
                 45 
                 46 
                 47 
                 48 
                 49 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.03 
                 72.3 
                 71.58 
                 72.23 
                 72.47 
                 72.09 
               
               
                   
                 Al 2 O 3   
                 12.77 
                 11.58 
                 11.7 
                 11.62 
                 11.54 
                 12.05 
               
               
                   
                 B 2 O 3   
                 1.72 
                 0 
                 1.25 
                 0 
                 0 
                 0 
               
               
                   
                 MgO 
                 3.82 
                 4.97 
                 4.86 
                 5.56 
                 5.24 
                 5.47 
               
               
                   
                 CaO 
                 4.89 
                 5.68 
                 5.26 
                 5.27 
                 5.35 
                 4.66 
               
               
                   
                 SrO 
                 1.18 
                 1.28 
                 1.4 
                 0.96 
                 0.72 
                 1.84 
               
               
                   
                 BaO 
                 3.44 
                 4.04 
                 3.8 
                 4.2 
                 4.53 
                 3.75 
               
               
                   
                 SnO 2   
                 0.12 
                 0.11 
                 0.13 
                 0.11 
                 0.11 
                 0.1 
               
               
                   
                 Fe 2 O 3   
                 0.01 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.01 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.04 
                 1.38 
                 1.31 
                 1.38 
                 1.37 
                 1.3 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 0.57 
                 4.39 
                 3.67 
                 4.37 
                 4.3 
                 3.67 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 86.28 
                 83.88 
                 84.33 
                 83.85 
                 84.01 
                 84.14 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.29 
                 0.31 
                 0.32 
                 0.35 
                 0.33 
                 0.35 
               
               
                 Properties 
                 Strain 
                 750 
                 762 
                 739 
                 757 
                 761 
                 764 
               
               
                   
                 Anneal 
                 803 
                 816 
                 794 
                 810 
                 814 
                 818 
               
               
                   
                 Soft (ppv) 
                   
                 1055.1 
                 1035.4 
                 1050.4 
                 1057.2 
                 1047 
               
               
                   
                 CTE (disk) 
                 35.1 
                 37.2 
                 37.2 
                 36.6 
                 36.6 
                 37.2 
               
               
                   
                 Density 
                   
                 2.625 
                 2.614 
                 2.623 
                 2.625 
                 2.63 
               
               
                   
                 Young&#39;s modulus 
                   
                 12.086 
                 11.984 
                 12.124 
                 12.194 
               
               
                   
                 specific modulus 
                   
                 31.7 
                 31.6 
                 31.9 
                 32 
               
               
                 Viscosity 
                 A 
                 −3.2039 
                 −3.224 
                 −2.978 
                 −3.099 
                 −3.327 
                 −3.085 
               
               
                   
                 B 
                 7359.53 
                 7477.8 
                 6940.6 
                 7233.1 
                 7780 
                 7131.02 
               
               
                   
                 To 
                 369.45 
                 353.2 
                 371.6 
                 364.2 
                 323.7 
                 379.69 
               
               
                   
                 200 poise 
                 1706 
                 1707 
                 1686 
                 1704 
                 1706 
                 1704 
               
               
                   
                 400 poise 
                 1637 
                 1637 
                 1615 
                 1633 
                 1636 
                 1634 
               
               
                   
                 35000 poise 
                 1319 
                 1316 
                 1294 
                 1311 
                 1312 
                 1314 
               
               
                 Gradient boat 
                 internal 
                 1210 
                 1200 
                 1190 
                 1210 
                 1200 
                 1235 
               
               
                   
                 internal viscosity 
                 356215.2 
                 404256.1 
                 318195.5 
                 283651.6 
                 355826.3 
                 178793.4 
               
               
                   
                 T(35 kp) − T(liq) 
                 109 
                 116 
                 104 
                 101 
                 112 
                 79 
               
               
                   
               
             
          
           
               
                 Example 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.99 
                 72.8 
                 72.66 
                 73.6 
                 71.99 
                 71.7 
               
               
                   
                 Al 2 O 3   
                 12.5 
                 11.38 
                 11.43 
                 11.38 
                 11.55 
                 12.49 
               
               
                   
                 B 2 O 3   
                 0.5 
                 0 
                 0 
                 0 
                 1.64 
                 1.25 
               
               
                   
                 MgO 
                 4.75 
                 5.12 
                 5.15 
                 4.73 
                 4.68 
                 4.75 
               
               
                   
                 CaO 
                 5.1 
                 5.33 
                 4.8 
                 5.1 
                 5.42 
                 5 
               
               
                   
                 SrO 
                 1.3 
                 1.14 
                 2.22 
                 1.32 
                 1.97 
                 2.35 
               
               
                   
                 BaO 
                 3.7 
                 4.08 
                 3.58 
                 3.74 
                 2.61 
                 2.25 
               
               
                   
                 SnO 2   
                 0.13 
                 0.11 
                 0.11 
                 0.12 
                 0.12 
                 0.16 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.02 
                 0.01 
                 0.01 
                 0.02 
               
               
                   
                 ZrO 2   
                 0 
                 0.02 
                 0.02 
                 0 
                 0 
                 0.03 
               
               
                   
                 RO/Al 2 O 3   
                 1.19 
                 1.38 
                 1.38 
                 1.31 
                 1.27 
                 1.15 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 2.36 
                 4.29 
                 4.32 
                 3.51 
                 3.18 
                 1.88 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.91 
                 84.18 
                 84.09 
                 84.98 
                 84.93 
                 85.26 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.33 
                 0.33 
                 0.32 
                 0.32 
                 0.33 
               
               
                 Properties 
                 Strain 
                 762 
                 761 
                 762 
                 765 
                 742 
                 749 
               
               
                   
                 Anneal 
                 817 
                 815 
                 816 
                 819 
                 798 
                 804 
               
               
                   
                 Soft (ppv) 
                 1057.8 
                 1058.3 
                 1058.2 
                 1060.3 
                 1042.4 
                 1043.7 
               
               
                   
                 CTE (disk) 
                 34.9 
                 35.5 
                 36.9 
                 35.8 
                 35.1 
                 34.2 
               
               
                   
                 Density 
                 2.604 
                 2.618 
                 2.622 
                 2.608 
                 2.567 
                 2.581 
               
               
                   
                 Young&#39;s modulus 
                 12.12 
                 12.03 
                 12.099 
                 12.025 
                 11.921 
               
               
                   
                 specific modulus 
                 32.1 
                 31.7 
                 31.8 
                 31.8 
                 32 
                 0 
               
               
                 Viscosity 
                 A 
                 −3.098 
                 −3.374 
                 −3.181 
                 −3.449 
                 −2.907 
                 −3.169 
               
               
                   
                 B 
                 7091.4 
                 7781.6 
                 7401.1 
                 7934.3 
                 6863.9 
                 7018.1 
               
               
                   
                 To 
                 391.2 
                 338.5 
                 363.3 
                 337.7 
                 380.6 
                 391 
               
               
                   
                 200 poise 
                 1705 
                 1710 
                 1713 
                 1718 
                 1699 
                 1674 
               
               
                   
                 400 poise 
                 1635 
                 1641 
                 1643 
                 1649 
                 1627 
                 1607 
               
               
                   
                 35000 poise 
                 1319 
                 1321 
                 1321 
                 1330 
                 1302 
                 1301 
               
               
                 Gradient boat 
                 internal 
                 1210 
                 1215 
                 1210 
                 1240 
                 1230 
                 1225 
               
               
                   
                 internal viscosity 
                 365361.7 
                 319181.5 
                 363172.2 
                 221012.5 
                 149238.4 
                 176192.7 
               
               
                   
                 T(35 kp) − T(liq) 
                 109 
                 106 
                 111 
                 90 
                 72 
                 76 
               
               
                   
               
             
          
           
               
                 Example 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.47 
                 72.75 
                 72.71 
                 71.85 
                 70.99 
                 72.83 
               
               
                   
                 Al 2 O 3   
                 11.42 
                 11.68 
                 11.41 
                 11.57 
                 11.79 
                 11.37 
               
               
                   
                 B 2 O 3   
                 1 
                 0 
                 0 
                 0 
                 1.2 
                 0 
               
               
                   
                 MgO 
                 4.76 
                 4.84 
                 4.95 
                 5.56 
                 5.57 
                 4.87 
               
               
                   
                 CaO 
                 5.13 
                 5.08 
                 5.45 
                 5.49 
                 5.36 
                 5.53 
               
               
                   
                 SrO 
                 1.33 
                 3.06 
                 1.5 
                 1.22 
                 1.84 
                 0.93 
               
               
                   
                 BaO 
                 3.76 
                 2.42 
                 3.82 
                 4.15 
                 3.08 
                 4.31 
               
               
                   
                 SnO 2   
                 0.12 
                 0.12 
                 0.11 
                 0.11 
                 0.11 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.01 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0 
                 0.02 
                 0.02 
                 0.02 
                 0.03 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.31 
                 1.32 
                 1.38 
                 1.42 
                 1.34 
                 1.38 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.6 
                 3.72 
                 4.31 
                 4.85 
                 4.11 
                 4.27 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.74 
                 84.43 
                 84.12 
                 83.42 
                 83.79 
                 84.2 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.31 
                 0.31 
                 0.34 
                 0.35 
                 0.31 
               
               
                 Properties 
                 Strain 
                 752 
                 764 
                 759 
                 760 
                 744 
                 760 
               
               
                   
                 Anneal 
                 809 
                 818 
                 814 
                 813 
                 796 
                 814 
               
               
                   
                 Soft (ppv) 
                 1058.2 
                 1056.5 
                 1055.8 
                 1052.3 
                 1034.1 
                 1059.6 
               
               
                   
                 CTE (disk) 
                 34.8 
                 36.1 
                 37.2 
                 38.3 
                 36.1 
                 36.6 
               
               
                   
                 Density 
                 2.595 
                 2.598 
                 2.62 
                 2.628 
                 2.6 
                 2.621 
               
               
                   
                 Young&#39;s modulus 
                 11.92 
                 11.927 
                 12.288 
                 12.14 
                 12.051 
                 12.01 
               
               
                   
                 specific modulus 
                 31.7 
                 31.7 
                 32.3 
                 31.9 
                 32 
                 31.6 
               
               
                 Viscosity 
                 A 
                 −3.053 
                 −3.214 
                 −3.04 
                 −3.017 
                 −3.07 
                 −3.315 
               
               
                   
                 B 
                 7293.1 
                 7452.5 
                 7104.2 
                 6965.6 
                 7012.4 
                 7912.6 
               
               
                   
                 To 
                 358.8 
                 357.5 
                 382.9 
                 390.6 
                 370.9 
                 314.4 
               
               
                   
                 200 poise 
                 1721 
                 1709 
                 1713 
                 1700 
                 1676 
                 1723 
               
               
                   
                 400 poise 
                 1648 
                 1639 
                 1642 
                 1630 
                 1607 
                 1652 
               
               
                   
                 35000 poise 
                 1319 
                 1318 
                 1320 
                 1312 
                 1292 
                 1321 
               
               
                 Gradient boat 
                 internal 
                 1240 
                 1235 
                 1210 
                 1210 
                 1195 
                 1210 
               
               
                   
                 internal viscosity 
                 167235.2 
                 190054.2 
                 354232.1 
                 304687.3 
                 274891.6 
                 331109 
               
               
                   
                 T(35 kp) − T(liq) 
                 79 
                 83 
                 110 
                 102 
                 97 
                 111 
               
               
                   
               
             
          
           
               
                 Example 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 70.77 
                 72.3 
                 71.68 
                 72.37 
                 73.61 
                 71.53 
               
               
                   
                 Al 2 O 3   
                 11.9 
                 11.84 
                 12.13 
                 12.12 
                 12.08 
                 11.9 
               
               
                   
                 B 2 O 3   
                 1.06 
                 0 
                 0 
                 0 
                 0 
                 1.35 
               
               
                   
                 MgO 
                 6 
                 5.01 
                 5.71 
                 4.92 
                 4.51 
                 4.37 
               
               
                   
                 CaO 
                 5.34 
                 5.58 
                 5.63 
                 5.66 
                 4.85 
                 5.36 
               
               
                   
                 SrO 
                 1.89 
                 2.1 
                 2.17 
                 2.75 
                 1.26 
                 1.38 
               
               
                   
                 BaO 
                 2.87 
                 3.01 
                 2.52 
                 2.02 
                 3.56 
                 3.97 
               
               
                   
                 SnO 2   
                 0.11 
                 0.12 
                 0.12 
                 0.12 
                 0.12 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.03 
                 0.02 
                 0.02 
                 0.02 
                 0.01 
                 0.01 
               
               
                   
                 ZrO 2   
                 0.03 
                 0.02 
                 0.03 
                 0.02 
                 0 
                 0.01 
               
               
                   
                 RO/Al 2 O 3   
                 1.35 
                 1.33 
                 1.32 
                 1.27 
                 1.17 
                 1.27 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 4.24 
                 3.86 
                 3.9 
                 3.23 
                 2.1 
                 3.22 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.56 
                 84.14 
                 83.81 
                 84.49 
                 85.69 
                 84.57 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.37 
                 0.32 
                 0.36 
                 0.32 
                 0.32 
                 0.29 
               
               
                 Properties 
                 Strain 
                 742 
                 766 
                 758 
                 767 
                 776 
                 745 
               
               
                   
                 Anneal 
                 795 
                 820 
                 815 
                 820 
                 830 
                 800 
               
               
                   
                 Soft (ppv) 
                 1029.6 
                 1057.6 
                 1052.7 
                 1059.5 
                 1077.1 
                 1043.5 
               
               
                   
                 CTE (disk) 
                 36.3 
                 35.9 
                 36.1 
                 36 
                 35.8 
                 37 
               
               
                   
                 Density 
                 2.603 
                 2.604 
                 2.597 
                 2.586 
                 2.591 
                 2.603 
               
               
                   
                 Young&#39;s modulus 
                 12.136 
                 12.137 
                 12.308 
                 12.258 
                 12.165 
                 11.92 
               
               
                   
                 specific modulus 
                 32.1 
                 32.1 
                 32.7 
                 32.7 
                 32.4 
                 31.6 
               
               
                 Viscosity 
                 A 
                 −3.035 
                 −2.991 
                 −3.143 
                 −3.049 
                 −3.566 
                 −2.943 
               
               
                   
                 B 
                 6870.8 
                 7115.9 
                 6986.1 
                 7170.6 
                 8149.3 
                 6909.4 
               
               
                   
                 To 
                 379.2 
                 368.7 
                 398.3 
                 370.2 
                 334.5 
                 379.8 
               
               
                   
                 200 poise 
                 1667 
                 1713 
                 1682 
                 1710 
                 1723 
                 1697 
               
               
                   
                 400 poise 
                 1598 
                 1641 
                 1614 
                 1639 
                 1656 
                 1626 
               
               
                   
                 35000 poise 
                 1286 
                 1313 
                 1307 
                 1315 
                 1339 
                 1303 
               
               
                 Gradient boat 
                 internal 
                 1205 
                 1220 
                 1220 
                 1235 
                 1265 
                 1190 
               
               
                   
                 internal viscosity 
                 192829.9 
                 233272.2 
                 228564.1 
                 174834.9 
                 155589.2 
                 384607.5 
               
               
                   
                 T(35 kp) − T(liq) 
                 81 
                 93 
                 87 
                 80 
                 74 
                 113 
               
               
                   
               
             
          
           
               
                 Example 
                 68 
                 69 
                 70 
                 71 
                 72 
                 73 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.76 
                 72.75 
                 70.78 
                 71.47 
                 72.9 
                 71.8 
               
               
                   
                 Al 2 O 3   
                 11.26 
                 11.42 
                 11.85 
                 11.87 
                 11.69 
                 11.49 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 0.87 
                 0 
                 0 
                 0 
               
               
                   
                 MgO 
                 5.34 
                 5.07 
                 4.97 
                 5.54 
                 4.83 
                 5.61 
               
               
                   
                 CaO 
                 5.75 
                 5.34 
                 5.77 
                 5.52 
                 5.25 
                 5.48 
               
               
                   
                 SrO 
                 1.52 
                 0.63 
                 1.47 
                 1.23 
                 1.37 
                 1.44 
               
               
                   
                 BaO 
                 4.18 
                 4.63 
                 4.12 
                 4.2 
                 3.83 
                 3.98 
               
               
                   
                 SnO 2   
                 0.16 
                 0.11 
                 0.14 
                 0.11 
                 0.12 
                 0.16 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.01 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0.02 
                 0.03 
                 0 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.49 
                 1.37 
                 1.38 
                 1.39 
                 1.31 
                 1.44 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 5.53 
                 4.25 
                 4.52 
                 4.62 
                 3.59 
                 5.02 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.02 
                 84.17 
                 83.36 
                 83.34 
                 84.59 
                 83.29 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.32 
                 0.3 
                 0.34 
                 0.32 
                 0.34 
               
               
                 Properties 
                 Strain 
                 751 
                 761 
                 742 
                 757 
                 765 
                 755 
               
               
                   
                 Anneal 
                 805 
                 815 
                 797 
                 810 
                 819 
                 808 
               
               
                   
                 Soft (ppv) 
                 1046 
                 1058.3 
                 1040.1 
                 1047.9 
                   
                 1048 
               
               
                   
                 CTE (disk) 
                 39.5 
                 37.3 
                 38.7 
                 37.8 
                 36.1 
                 38.6 
               
               
                   
                 Density 
                 2.641 
                 2.627 
                 2.632 
                 2.637 
                 2.6 
                 2.631 
               
               
                   
                 Young&#39;s modulus 
                   
                 12.013 
                   
                 12.237 
                 12.124 
               
               
                   
                 specific modulus 
                   
                 31.5 
                   
                 32 
                 32.2 
               
               
                 Viscosity 
                 A 
                 −3.1715 
                 −2.639 
                 −2.8291 
                 −2.87 
                 −2.887 
                 −3.2947 
               
               
                   
                 B 
                 7306.29 
                 6448.7 
                 6603.21 
                 6677.3 
                 6946 
                 7613.94 
               
               
                   
                 To 
                 355.18 
                 421.2 
                 398.09 
                 404.8 
                 391.2 
                 333.99 
               
               
                   
                 200 poise 
                 1690 
                 1727 
                 1685 
                 1696 
                 1730 
                 1695 
               
               
                   
                 400 poise 
                 1621 
                 1652 
                 1614 
                 1625 
                 1657 
                 1625 
               
               
                   
                 35000 poise 
                 1302 
                 1319 
                 1294 
                 1305 
                 1326 
                 1305 
               
               
                 Gradient boat 
                 internal 
                 1200 
                 1200 
                 1180 
                 1230 
                 1210 
                 1210 
               
               
                   
                 internal viscosity 
                 299805.3 
                 437827.5 
                 412928.1 
                 166623.1 
                 394590 
                 249409.6 
               
               
                   
                 T(35 kp) − T(liq) 
                 102 
                 119 
                 114 
                 75 
                 116 
                 95 
               
               
                   
               
             
          
           
               
                 Example 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.39 
                 73.19 
                 72.74 
                 71.85 
                 71.4 
                 71.79 
               
               
                   
                 Al 2 O 3   
                 12.32 
                 11.54 
                 11.38 
                 10.79 
                 11.71 
                 11.53 
               
               
                   
                 B 2 O 3   
                 0.5 
                 0 
                 0 
                 0 
                 1.55 
                 1.55 
               
               
                   
                 MgO 
                 4.68 
                 4.81 
                 5.18 
                 5.44 
                 4.86 
                 4.8 
               
               
                   
                 CaO 
                 5.03 
                 5.19 
                 5.25 
                 5.89 
                 5.38 
                 5.3 
               
               
                   
                 SrO 
                 1.28 
                 1.34 
                 0.04 
                 1.55 
                 1.93 
                 1.9 
               
               
                   
                 BaO 
                 3.65 
                 3.79 
                 5.26 
                 4.27 
                 3.05 
                 3 
               
               
                   
                 SnO 2   
                 0.13 
                 0.12 
                 0.11 
                 0.16 
                 0.12 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.01 
                 0.02 
                 0.02 
                 0.01 
                 0.01 
               
               
                   
                 ZrO 2   
                 0 
                 0 
                 0.02 
                 0.02 
                 0 
                 0 
               
               
                   
                 RO/Al 2 O 3   
                 1.19 
                 1.31 
                 1.38 
                 1.59 
                 1.3 
                 1.3 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 2.33 
                 3.59 
                 4.35 
                 6.36 
                 3.57 
                 3.52 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 85.14 
                 84.73 
                 84.12 
                 82.64 
                 84.42 
                 84.63 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.32 
                 0.33 
                 0.32 
                 0.32 
                 0.32 
               
               
                 Properties 
                 Strain 
                 762 
                 770 
                 760 
                 748 
                 743 
                 742 
               
               
                   
                 Anneal 
                 817 
                 822 
                 814 
                 801 
                 797 
                 796 
               
               
                   
                 Soft (ppv) 
                 1060.3 
                 1068.8 
                 1058.4 
                 1043 
                 1040 
                 1041.7 
               
               
                   
                 CTE (disk) 
                 35.8 
                 35.7 
                 36.5 
                 39.8 
                 35.6 
                 34.9 
               
               
                   
                 Density 
                 2.596 
                 2.6 
                 2.63 
                 2.645 
                 2.586 
                 2.584 
               
               
                   
                 Young&#39;s modulus 
                 12.046 
                 12.039 
                 11.954 
                   
                 11.937 
                 11.918 
               
               
                   
                 specific modulus 
                 32 
                 31.9 
                 31.3 
                   
                 31.8 
                 31.8 
               
               
                 Viscosity 
                 A 
                 −3.115 
                 −3.715 
                 −3.007 
                 −3.2794 
                 −3.16 
                 −3.089 
               
               
                   
                 B 
                 7142 
                 8889.8 
                 7290.9 
                 7568.49 
                 7253.8 
                 7373 
               
               
                   
                 To 
                 393.1 
                 251 
                 346.7 
                 329.91 
                 358.9 
                 332.6 
               
               
                   
                 200 poise 
                 1712 
                 1729 
                 1720 
                 1686 
                 1687 
                 1700 
               
               
                   
                 400 poise 
                 1642 
                 1658 
                 1647 
                 1617 
                 1618 
                 1628 
               
               
                   
                 35000 poise 
                 1326 
                 1327 
                 1312 
                 1297 
                 1300 
                 1299 
               
               
                 Gradient boat 
                 internal 
                 1230 
                 1235 
                 1195 
                 1205 
                 1230 
                 1220 
               
               
                   
                 internal viscosity 
                 262346.3 
                 208617 
                 387007 
                 234106.4 
                 146951 
                 165783.7 
               
               
                   
                 T(35 kp) − T(liq) 
                 96 
                 92 
                 117 
                 92 
                 70 
                 79 
               
               
                   
               
             
          
           
               
                 Example 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.18 
                 73.58 
                 72.47 
                 72.1 
                 71.96 
                 71.97 
               
               
                   
                 Al 2 O 3   
                 12.2 
                 11.77 
                 11.46 
                 12.05 
                 12.02 
                 11.58 
               
               
                   
                 B 2 O 3   
                 0 
                 0.5 
                 0 
                 0 
                 0 
                 0.84 
               
               
                   
                 MgO 
                 4.91 
                 4.48 
                 5.34 
                 5.47 
                 4.98 
                 4.68 
               
               
                   
                 CaO 
                 5.52 
                 4.81 
                 5.3 
                 5.16 
                 5.23 
                 5.47 
               
               
                   
                 SrO 
                 2.07 
                 1.22 
                 0.37 
                 1.34 
                 2.15 
                 1.39 
               
               
                   
                 BaO 
                 2.96 
                 3.49 
                 4.9 
                 3.75 
                 3.49 
                 3.9 
               
               
                   
                 SnO 2   
                 0.12 
                 0.13 
                 0.11 
                 0.1 
                 0.12 
                 0.14 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.02 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0 
                 0.02 
                 0.02 
                 0.03 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.27 
                 1.19 
                 1.39 
                 1.3 
                 1.32 
                 1.33 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.26 
                 2.24 
                 4.45 
                 3.67 
                 3.83 
                 3.89 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.38 
                 85.78 
                 83.93 
                 84.15 
                 83.98 
                 84.26 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.32 
                 0.34 
                 0.35 
                 0.31 
                 0.3 
               
               
                 Properties 
                 Strain 
                 767 
                 766 
                 761 
                 764 
                 766 
                 748 
               
               
                   
                 Anneal 
                 821 
                 822 
                 815 
                 817 
                 819 
                 801 
               
               
                   
                 Soft (ppv) 
                 1059 
                 1073.2 
                 1056.3 
                 1046 
                 1059.6 
                 1050.8 
               
               
                   
                 CTE (disk) 
                 35.7 
                 33.7 
                 37.3 
                 37.3 
                 37.1 
                 38.6 
               
               
                   
                 Density 
                 2.599 
                 2.577 
                 2.62 
                 2.613 
                 2.616 
                 2.613 
               
               
                   
                 Young&#39;s modulus 
                 12.162 
                 11.981 
                 11.948 
                   
                 12.202 
               
               
                   
                 specific modulus 
                 32.3 
                 32.1 
                 31.4 
                   
                 32.2 
               
               
                 Viscosity 
                 A 
                 −2.943 
                 −3.293 
                 −3.344 
                 −2.967 
                 −3.087 
                 −2.6835 
               
               
                   
                 B 
                 6934.4 
                 7631.6 
                 7736.8 
                 6855.99 
                 7170.9 
                 6479.42 
               
               
                   
                 To 
                 388.4 
                 359.5 
                 336.1 
                 403.9 
                 369.3 
                 412.79 
               
               
                   
                 200 poise 
                 1711 
                 1724 
                 1707 
                 1705 
                 1700 
                 1713 
               
               
                   
                 400 poise 
                 1639 
                 1654 
                 1637 
                 1635 
                 1630 
                 1639 
               
               
                   
                 35000 poise 
                 1315 
                 1333 
                 1317 
                 1317 
                 1309 
                 1309 
               
               
                 Gradient boat 
                 internal 
                 1240 
                 1245 
                 1220 
                 1220 
                 1220 
                 1195 
               
               
                   
                 internal viscosity 
                 158412.7 
                 211547.4 
                 256464 
                 271593.3 
                 219994.1 
                 398087.8 
               
               
                   
                 T(35 kp) − T(liq) 
                 75 
                 88 
                 97 
                 97 
                 89 
                 114 
               
               
                   
               
             
          
           
               
                 Example 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.31 
                 71.28 
                 71.2 
                 72.21 
                 71.69 
                 72.77 
               
               
                   
                 Al 2 O 3   
                 11.86 
                 12.27 
                 12.13 
                 11.56 
                 11.89 
                 11.38 
               
               
                   
                 B 2 O 3   
                 1.35 
                 1.72 
                 0.5 
                 0 
                 1.25 
                 0 
               
               
                   
                 MgO 
                 5.21 
                 4.19 
                 6.03 
                 5.43 
                 4.85 
                 5.56 
               
               
                   
                 CaO 
                 5.35 
                 5.34 
                 5.28 
                 5.36 
                 5.11 
                 3.86 
               
               
                   
                 SrO 
                 2.01 
                 1.29 
                 2.17 
                 0.74 
                 1.45 
                 3.09 
               
               
                   
                 BaO 
                 2.76 
                 3.76 
                 2.52 
                 4.55 
                 3.6 
                 3.19 
               
               
                   
                 SnO 2   
                 0.12 
                 0.12 
                 0.12 
                 0.11 
                 0.12 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.03 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.01 
                 0.01 
                 0.03 
                 0.02 
                 0 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.29 
                 1.19 
                 1.32 
                 1.39 
                 1.26 
                 1.38 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.52 
                 2.35 
                 3.89 
                 4.52 
                 3.16 
                 4.32 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.31 
                 85.01 
                 83.75 
                 83.77 
                 84.64 
                 84.15 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.34 
                 0.29 
                 0.38 
                 0.34 
                 0.32 
                 0.35 
               
               
                 Properties 
                 Strain 
                 745 
                 743 
                 750 
                 759 
                 740 
                 762 
               
               
                   
                 Anneal 
                 799 
                 798 
                 804 
                 813 
                 794 
                 816 
               
               
                   
                 Soft (ppv) 
                 1039.6 
                 1044.9 
                 1040 
                 1055.3 
                 1038.7 
                 1059 
               
               
                   
                 CTE (disk) 
                 35.7 
                 34.8 
                 37.7 
                 36.2 
                 36.2 
                 36.3 
               
               
                   
                 Density 
                 2.583 
                 2.597 
                 2.6 
                 2.627 
                 2.61 
                 2.615 
               
               
                   
                 Young&#39;s modulus 
                 12.246 
                 11.874 
                   
                 12.085 
                 12.033 
                 12.076 
               
               
                   
                 specific modulus 
                 32.7 
                 31.5 
                   
                 31.7 
                 31.8 
                 31.8 
               
               
                 Viscosity 
                 A 
                 −2.812 
                 −3.025 
                 −3.1872 
                 −3.18 
                 −2.898 
                 −3.169 
               
               
                   
                 B 
                 6516.6 
                 7014.5 
                 7081.73 
                 7409.1 
                 6712.1 
                 7419 
               
               
                   
                 To 
                 413 
                 375.5 
                 377.63 
                 357.2 
                 392 
                 360 
               
               
                   
                 200 poise 
                 1688 
                 1693 
                 1668 
                 1709 
                 1683 
                 1716 
               
               
                   
                 400 poise 
                 1617 
                 1622 
                 1601 
                 1639 
                 1612 
                 1646 
               
               
                   
                 35000 poise 
                 1299 
                 1302 
                 1294 
                 1316 
                 1294 
                 1322 
               
               
                 Gradient boat 
                 internal 
                 1205 
                 1185 
                 1210 
                 1220 
                 1210 
                 1225 
               
               
                   
                 internal viscosity 
                 260633.5 
                 436742.5 
                 209272 
                 255431.2 
                 203002.4 
                 255787.1 
               
               
                   
                 T(35 kp) − T(liq) 
                 94 
                 117 
                 84 
                 96 
                 84 
                 97 
               
               
                   
               
             
          
           
               
                 Example 
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.39 
                 71.74 
                 71.2 
                 73.78 
                 71.65 
                 72.79 
               
               
                   
                 Al 2 O 3   
                 11.55 
                 11.37 
                 11.91 
                 11.88 
                 12.18 
                 12.14 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 1.65 
                 0.63 
                 0 
                 0.5 
               
               
                   
                 MgO 
                 5.05 
                 5.83 
                 4.81 
                 4.3 
                 6.07 
                 4.62 
               
               
                   
                 CaO 
                 5.48 
                 5.48 
                 5.58 
                 4.64 
                 5.49 
                 4.95 
               
               
                   
                 SrO 
                 1.66 
                 1.08 
                 2.03 
                 1.16 
                 2.34 
                 1.26 
               
               
                   
                 BaO 
                 3.72 
                 4.32 
                 2.69 
                 3.46 
                 2.11 
                 3.59 
               
               
                   
                 SnO 2   
                 0.11 
                 0.11 
                 0.12 
                 0.11 
                 0.12 
                 0.13 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.04 
                 0.01 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.01 
                 0.03 
                 0 
                 0.02 
                 0.02 
                 0 
               
               
                   
                 RO/Al 2 O 3   
                 1.38 
                 1.47 
                 1.27 
                 1.14 
                 1.31 
                 1.19 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 4.36 
                 5.34 
                 3.25 
                 1.69 
                 3.83 
                 2.29 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 83.94 
                 83.11 
                 84.5 
                 86.2 
                 83.83 
                 85.36 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.32 
                 0.35 
                 0.32 
                 0.32 
                 0.38 
                 0.32 
               
               
                 Properties 
                 Strain 
                 760 
                 753 
                 741 
                 763 
                 765 
                 764 
               
               
                   
                 Anneal 
                 813 
                 806 
                 796 
                 820 
                 817 
                 819 
               
               
                   
                 Soft (ppv) 
                 1055.4 
                 1044.7 
                 1039.2 
                 1070.2 
                 1049.5 
                 1062.7 
               
               
                   
                 CTE (disk) 
                 36.9 
                 37.8 
                 36 
                 34.3 
                 36.1 
                 34.9 
               
               
                   
                 Density 
                 2.622 
                 2.637 
                 2.578 
                 2.574 
                 2.591 
                 2.589 
               
               
                   
                 Young&#39;s modulus 
                 12.164 
                 12.119 
                 11.97 
                 11.988 
                 12.446 
                 12.04 
               
               
                   
                 specific modulus 
                 32 
                 31.7 
                 32 
                 32.1 
                 33.1 
                 32.1 
               
               
                 Viscosity 
                 A 
                 −3.214 
                 −3.086 
                 −2.964 
                 −2.597 
                 −3.309 
                 −3.074 
               
               
                   
                 B 
                 7473.4 
                 7079.3 
                 6900.9 
                 6453.9 
                 7354.2 
                 7152.6 
               
               
                   
                 To 
                 354.4 
                 383.5 
                 376.5 
                 432.9 
                 364.9 
                 386.7 
               
               
                   
                 200 poise 
                 1709 
                 1698 
                 1687 
                 1751 
                 1676 
                 1717 
               
               
                   
                 400 poise 
                 1639 
                 1628 
                 1616 
                 1674 
                 1609 
                 1647 
               
               
                   
                 35000 poise 
                 1318 
                 1311 
                 1296 
                 1337 
                 1301 
                 1326 
               
               
                 Gradient boat 
                 internal 
                 1215 
                 1210 
                 1210 
                 1240 
                 1225 
                 1230 
               
               
                   
                 internal viscosity 
                 295081.1 
                 301575.6 
                 206739.8 
                 250845.8 
                 174341.6 
                 255669.6 
               
               
                   
                 T(35 kp) − T(liq) 
                 103 
                 101 
                 86 
                 97 
                 76 
                 96 
               
               
                   
               
             
          
           
               
                 Example 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.33 
                 71.5 
                 71.5 
                 71.06 
                 70.87 
                 71.13 
               
               
                   
                 Al 2 O 3   
                 11.69 
                 11.78 
                 11.75 
                 11.98 
                 11.75 
                 11.2 
               
               
                   
                 B 2 O 3   
                 0 
                 0.85 
                 1.99 
                 1.85 
                 1.31 
                 0.69 
               
               
                   
                 MgO 
                 5.26 
                 4.77 
                 4.2 
                 4.45 
                 5.53 
                 5.84 
               
               
                   
                 CaO 
                 5.34 
                 5.55 
                 5.28 
                 5.77 
                 5.4 
                 5.52 
               
               
                   
                 SrO 
                 1.24 
                 1.41 
                 2.65 
                 1.7 
                 1.77 
                 1.04 
               
               
                   
                 BaO 
                 4 
                 3.96 
                 2.49 
                 3.03 
                 3.22 
                 4.41 
               
               
                   
                 SnO 2   
                 0.11 
                 0.14 
                 0.12 
                 0.12 
                 0.11 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.01 
                 0.02 
                 0.01 
                 0.01 
                 0.02 
                 0.05 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0.01 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.36 
                 1.33 
                 1.24 
                 1.25 
                 1.35 
                 1.5 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 4.15 
                 3.94 
                 2.93 
                 3.03 
                 4.23 
                 5.65 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.02 
                 83.99 
                 84.94 
                 84.61 
                 83.72 
                 82.9 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.33 
                 0.3 
                 0.29 
                 0.3 
                 0.35 
                 0.35 
               
               
                 Properties 
                 Strain 
                 763 
                 748 
                 737 
                 740 
                 742 
                 741 
               
               
                   
                 Anneal 
                 816 
                 800 
                 793 
                 794 
                 794 
                 793 
               
               
                   
                 Soft (ppv) 
                 1056.4 
                 1046.7 
                 1037.9 
                 1037.3 
                 1032.8 
                 1031.1 
               
               
                   
                 CTE (disk) 
                 36.2 
                 37.5 
                 35.9 
                 36 
                 35.9 
                 34.9 
               
               
                   
                 Density 
                 2.621 
                 2.62 
                 2.574 
                 2.58 
                 2.601 
                 2.633 
               
               
                   
                 Young&#39;s modulus 
                 12.229 
                   
                 11.87 
                 12.06 
                 12.082 
                 12.053 
               
               
                   
                 specific modulus 
                 32.2 
                   
                 31.8 
                 32.2 
                 32 
                 31.6 
               
               
                 Viscosity 
                 A 
                 −2.965 
                 −2.7111 
                 −2.963 
                 −2.719 
                 −2.756 
                 −3.099 
               
               
                   
                 B 
                 6904.9 
                 6461.74 
                 6934 
                 6302.2 
                 6435.6 
                 7055.7 
               
               
                   
                 To 
                 402 
                 416 
                 373.1 
                 430.5 
                 406.1 
                 365.4 
               
               
                   
                 200 poise 
                 1713 
                 1705 
                 1690 
                 1686 
                 1679 
                 1672 
               
               
                   
                 400 poise 
                 1642 
                 1632 
                 1619 
                 1615 
                 1607 
                 1603 
               
               
                   
                 35000 poise 
                 1322 
                 1307 
                 1297 
                 1298 
                 1288 
                 1289 
               
               
                 Gradient boat 
                 internal 
                 1220 
                 1190 
                 1200 
                 1200 
                 1190 
                 1185 
               
               
                   
                 internal viscosity 
                 299362.9 
                 433911.6 
                 264567.4 
                 295796.8 
                 284263.2 
                 323378.8 
               
               
                   
                 T(35 kp) − T(liq) 
                 102 
                 117 
                 97 
                 98 
                 98 
                 104 
               
               
                   
               
             
          
           
               
                 Example 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 71.52 
                 73.74 
                 71.43 
                 73.55 
                 72.18 
                 71.34 
               
               
                   
                 Al 2 O 3   
                 12.44 
                 11.82 
                 11.43 
                 11.85 
                 11.86 
                 10.98 
               
               
                   
                 B 2 O 3   
                 1.72 
                 0 
                 0 
                 0.3 
                 0 
                 0 
               
               
                   
                 MgO 
                 4.08 
                 4.54 
                 6.1 
                 4.5 
                 5.52 
                 5.56 
               
               
                   
                 CaO 
                 5.19 
                 4.9 
                 5.44 
                 4.83 
                 5.39 
                 5.99 
               
               
                   
                 SrO 
                 1.25 
                 1.24 
                 1.43 
                 1.23 
                 1.59 
                 1.58 
               
               
                   
                 BaO 
                 3.65 
                 3.62 
                 3.96 
                 3.59 
                 3.3 
                 4.35 
               
               
                   
                 SnO 2   
                 0.12 
                 0.11 
                 0.16 
                 0.11 
                 0.11 
                 0.16 
               
               
                   
                 Fe 2 O 3   
                 0.01 
                 0.01 
                 0.02 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.14 
                 1.21 
                 1.48 
                 1.19 
                 1.33 
                 1.59 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 1.76 
                 2.48 
                 5.5 
                 2.31 
                 3.94 
                 6.5 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 85.43 
                 85.56 
                 82.86 
                 85.66 
                 84.04 
                 82.32 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.29 
                 0.32 
                 0.36 
                 0.32 
                 0.35 
                 0.32 
               
               
                 Properties 
                 Strain 
                 745 
                 770 
                 753 
                 768 
                 764 
                 750 
               
               
                   
                 Anneal 
                 798 
                 825 
                 806 
                 823 
                 816 
                 802 
               
               
                   
                 Soft (ppv) 
                   
                 1071.1 
                 1041 
                 1071.7 
                 1050.7 
                 1039 
               
               
                   
                 CTE (disk) 
                 36.4 
                 35.9 
                 38.2 
                 35.7 
                 36.7 
                 40.1 
               
               
                   
                 Density 
                   
                 2.59 
                 2.633 
                 2.589 
                 2.616 
                 2.652 
               
               
                   
                 Young&#39;s modulus 
                   
                 12.047 
                   
                 12.037 
                 12.292 
               
               
                   
                 specific modulus 
                   
                 32.1 
                   
                 32.1 
                 32.4 
               
               
                 Viscosity 
                 A 
                 −3.3669 
                 −3.093 
                 −3.1455 
                 −2.724 
                 −2.405 
                 −3.1246 
               
               
                   
                 B 
                 7769.3 
                 7315.2 
                 7160.06 
                 6678.5 
                 5903.2 
                 7195.68 
               
               
                   
                 To 
                 322.18 
                 375.6 
                 372.38 
                 418.1 
                 457.3 
                 356.84 
               
               
                   
                 200 poise 
                 1693 
                 1732 
                 1687 
                 1747 
                 1712 
                 1683 
               
               
                   
                 400 poise 
                 1624 
                 1660 
                 1618 
                 1672 
                 1636 
                 1613 
               
               
                   
                 35000 poise 
                 1304 
                 1333 
                 1304 
                 1337 
                 1307 
                 1295 
               
               
                 Gradient boat 
                 internal 
                 1190 
                 1235 
                 1200 
                 1250 
                 1210 
                 1190 
               
               
                   
                 internal viscosity 
                 385268 
                 262412.9 
                 320542.7 
                 201376.2 
                 273967.9 
                 325096.6 
               
               
                   
                 T(35 kp) − T(liq) 
                 114 
                 98 
                 104 
                 87 
                 97 
                 105 
               
               
                   
               
             
          
           
               
                 Example 
                 110 
                 111 
                 112 
                 113 
                 114 
                 115 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.75 
                 73.6 
                 72.81 
                 72.64 
                 72.5 
                 71.12 
               
               
                   
                 Al 2 O 3   
                 11.41 
                 11.74 
                 11.38 
                 11.37 
                 11.87 
                 11.82 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 0 
                 0 
                 0 
                 2.01 
               
               
                   
                 MgO 
                 4.92 
                 4.62 
                 4.93 
                 5.27 
                 4.91 
                 4.45 
               
               
                   
                 CaO 
                 5.54 
                 4.98 
                 5.46 
                 5.07 
                 5.33 
                 5.93 
               
               
                   
                 SrO 
                 1.17 
                 1.29 
                 1.37 
                 3.3 
                 1.39 
                 2.25 
               
               
                   
                 BaO 
                 4.06 
                 3.64 
                 3.9 
                 2.2 
                 3.87 
                 2.26 
               
               
                   
                 SnO 2   
                 0.11 
                 0.12 
                 0.11 
                 0.11 
                 0.12 
                 0.12 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.01 
                 0.02 
                 0.02 
                 0.01 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.02 
                 0 
                 0.02 
                 0.02 
                 0 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.38 
                 1.24 
                 1.38 
                 1.39 
                 1.31 
                 1.26 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 4.28 
                 2.79 
                 4.28 
                 4.47 
                 3.63 
                 3.13 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.16 
                 85.34 
                 84.19 
                 84.01 
                 84.37 
                 84.64 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.31 
                 0.32 
                 0.31 
                 0.33 
                 0.32 
                 0.3 
               
               
                 Properties 
                 Strain 
                 760 
                 772 
                 760 
                 760 
                 765 
                 735 
               
               
                   
                 Anneal 
                 814 
                 826 
                 815 
                 815 
                 820 
                 791 
               
               
                   
                 Soft (ppv) 
                 1056.3 
                 1071 
                 1054.1 
                 1056.4 
                   
                 1033.5 
               
               
                   
                 CTE (disk) 
                 36.7 
                 35.7 
                 36.6 
                 36.2 
                 36 
                 36.3 
               
               
                   
                 Density 
                 2.622 
                 2.599 
                 2.62 
                 2.599 
                 2.601 
                 2.568 
               
               
                   
                 Young&#39;s modulus 
                 12.073 
                 12.095 
                 12.127 
                 12.228 
                 12.146 
                 11.956 
               
               
                   
                 specific modulus 
                 31.7 
                 32.1 
                 31.9 
                 32.4 
                 32.2 
                 32.1 
               
               
                 Viscosity 
                 A 
                 −3.431 
                 −3.385 
                 −2.954 
                 −3.608 
                 −3.184 
                 −3.086 
               
               
                   
                 B 
                 7862.3 
                 7779.3 
                 6950.9 
                 8438.4 
                 7438.8 
                 7014.9 
               
               
                   
                 To 
                 335 
                 357.4 
                 394.2 
                 282.4 
                 357 
                 375.4 
               
               
                   
                 200 poise 
                 1707 
                 1726 
                 1717 
                 1710 
                 1713 
                 1678 
               
               
                   
                 400 poise 
                 1638 
                 1657 
                 1645 
                 1641 
                 1643 
                 1609 
               
               
                   
                 35000 poise 
                 1321 
                 1339 
                 1321 
                 1318 
                 1320 
                 1295 
               
               
                 Gradient boat 
                 internal 
                 1210 
                 1250 
                 1210 
                 1240 
                 1210 
                 1210 
               
               
                   
                 internal viscosity 
                 358497.2 
                 213956.8 
                 368424.2 
                 159966.9 
                 344152 
                 208499.1 
               
               
                   
                 T(35 kp) − T(liq) 
                 111 
                 89 
                 111 
                 78 
                 110 
                 85 
               
               
                   
               
             
          
           
               
                 Example 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
               
               
                   
               
             
          
           
               
                   
                 SiO 2   
                 72.29 
                 72.71 
                 71.88 
                 71.32 
                 72.33 
                 71.88 
               
               
                   
                 Al 2 O 3   
                 11.87 
                 11.48 
                 11.47 
                 11.64 
                 11.55 
                 11.97 
               
               
                   
                 B 2 O 3   
                 0 
                 0 
                 0 
                 0.85 
                 0 
                 0 
               
               
                   
                 MgO 
                 4.92 
                 4.95 
                 5.66 
                 4.87 
                 5.05 
                 5.74 
               
               
                   
                 CaO 
                 5.67 
                 5.39 
                 5.46 
                 5.67 
                 5.49 
                 5.36 
               
               
                   
                 SrO 
                 2.62 
                 1.46 
                 1.12 
                 1.44 
                 1.52 
                 1.89 
               
               
                   
                 BaO 
                 2.46 
                 3.82 
                 4.24 
                 4.05 
                 3.9 
                 3 
               
               
                   
                 SnO 2   
                 0.12 
                 0.15 
                 0.11 
                 0.14 
                 0.11 
                 0.11 
               
               
                   
                 Fe 2 O 3   
                 0.02 
                 0.02 
                 0.03 
                 0.01 
                 0.02 
                 0.02 
               
               
                   
                 ZrO 2   
                 0.03 
                 0.02 
                 0.02 
                 0 
                 0.02 
                 0.02 
               
               
                   
                 RO/Al 2 O 3   
                 1.32 
                 1.36 
                 1.44 
                 1.38 
                 1.38 
                 1.34 
               
               
                   
                 (RO − Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 3.8 
                 4.14 
                 5.01 
                 4.43 
                 4.41 
                 4.02 
               
               
                   
                 (SiO 2  + Al 2 O 3 )/(1 − B 2 O 3 /100) 
                 84.16 
                 84.19 
                 83.35 
                 83.67 
                 83.88 
                 83.85 
               
               
                   
                 MgO/(MgO + CaO + SrO + BaO) 
                 0.31 
                 0.32 
                 0.34 
                 0.3 
                 0.32 
                 0.36 
               
               
                 Properties 
                 Strain 
                 763 
                 763 
                 757 
                 744 
                 763 
                 762 
               
               
                   
                 Anneal 
                 818 
                 817 
                 810 
                 798 
                 814 
                 814 
               
               
                   
                 Soft (ppv) 
                 1057.3 
                 1055.8 
                 1049.1 
                 1042.4 
                 1055.7 
                 1051.6 
               
               
                   
                 CTE (disk) 
                 36 
                 36.6 
                 38.3 
                 38.4 
                 37.2 
                 35.7 
               
               
                   
                 Density 
                 2.598 
                 2.613 
                 2.634 
                 2.624 
                 2.623 
                 2.608 
               
               
                   
                 Young&#39;s modulus 
                 12.197 
                 12.08 
                 12.094 
                   
                 12.118 
                 12.297 
               
               
                   
                 specific modulus 
                 32.4 
                 31.9 
                 31.7 
                   
                 31.9 
                 32.5 
               
               
                 Viscosity 
                 A 
                 −2.921 
                 −3.036 
                 −3.121 
                 −2.745 
                 −3.031 
                 −2.606 
               
               
                   
                 B 
                 6826.5 
                 7156.8 
                 7213.1 
                 6495.63 
                 7108.6 
                 6152.6 
               
               
                   
                 To 
                 395.7 
                 373.8 
                 367.2 
                 406.26 
                 378.9 
                 446 
               
               
                   
                 200 poise 
                 1703 
                 1715 
                 1698 
                 1694 
                 1712 
                 1700 
               
               
                   
                 400 poise 
                 1632 
                 1643 
                 1628 
                 1621 
                 1641 
                 1627 
               
               
                   
                 35000 poise 
                 1310 
                 1318 
                 1308 
                 1297 
                 1317 
                 1306 
               
               
                 Gradient boat 
                 internal 
                 1240 
                 1210 
                 1220 
                 1185 
                 1200 
                 1225 
               
               
                   
                 internal viscosity 
                 146014.6 
                 333210 
                 217339.1 
                 394643.6 
                 423068.6 
                 195918.1 
               
               
                   
                 T(35 kp) − T(liq) 
                 70 
                 108 
                 88 
                 112 
                 117 
                 81 
               
               
                   
               
             
          
         
       
     
         [0055]    Various modifications and variations can be made to the materials, methods, and articles described herein. Other aspects of the materials, methods, and articles described herein will be apparent from consideration of the specification and practice of the materials, methods, and articles disclosed herein. It is intended that the specification and examples be considered as exemplary.