Abstract:
Glass compositions are provided that are useful in a variety of applications including, for example, electronics applications, reinforcement applications, and others. Some embodiments of glass compositions can provide desirable dielectric constants, desirable dissipation factors, and/or desirable mechanical properties while also having desirable fiber forming properties.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 14/226,885, filed Mar. 27, 2014, which is a continuation of U.S. patent application Ser. No. 13/229,012, filed on Sep. 9, 2011, now U.S. Pat. No. 8,697,591, issued on Apr. 15, 2014, which is a continuation-in-part of U.S. patent application Ser. No. 12/940,764, filed on Nov. 5, 2010, now U.S. Pat. No. 8,697,590, issued on Apr. 15, 2014, which is a continuation of U.S. patent application Ser. No. 11/610,761, filed on Dec. 14, 2006, now U.S. Pat. No. 7,829,490, which issued Nov. 9, 2010, the contents of which are hereby herein incorporated by reference in their entireties. 
     
    
     BACKGROUND 
       [0002]    This invention relates to glass compositions that can be used, for example, to form glass fibers. Such glass fibers can be used in a wide variety of end-use applications. 
         [0003]    For example, in some embodiments, glass fibers are adapted for formation into fibers that can be employed for reinforcing composite substrates comprising a printed circuit board (“PCB”). More particularly, some embodiments of the present invention relate to glass fiber reinforcements that have electrical properties that permit enhancing performance of a PCB. 
         [0004]    “D k ” is the dielectric constant of a material, also known as “permittivity” and is a measure of the ability of a material to store electric energy. A material to be used as a capacitor desirably has a relatively high D k , whereas a material to be used as part of a PCB substrate desirably has a low D k , particularly for high speed circuits. D k  is the ratio of the charge that would be stored (i.e., the capacitance) of a given material between two metal plates to the amount of charge that would be stored by a void (air or vacuum) between the same two metal plates. “D f ” or dissipation factor is the measure of the loss of power in a dielectric material. D f  is the ratio of the resistive loss component of the current to the capacitive component of current, and is equal to the tangent of the loss angle. For high speed circuitry, it is desired that the D f  of materials comprising a PCB substrate be relatively low. 
         [0005]    PCB&#39;s have commonly been reinforced with glass fibers of the “E-glass” family of compositions, which is based on “Standard Specification for Glass Fiber Strands” D 578 American Society for Testing and Materials. By this definition, E-glass for electronic applications contains 5 to 10 weight percent B 2 O 3 , which reflects recognition of the desirable effect of B 2 O 3  on dielectric properties of glass compositions. E-glass fibers for electronic applications typically have D k  in the range 6.7-7.3 at 1 MHz frequency. Standard electronic E-glass is also formulated to provide melting and forming temperatures conducive to practical manufacturing. Forming temperatures (the temperature at which the viscosity is 1000 poise), also referred to herein as T F , for commercial electronic E-glass are typically in the range of 1170° C.-1250° C. 
         [0006]    High performance printed circuit boards require substrate reinforcements having lower D k  compared to E-glass for better performance, i.e., less noise signal transmission, for applications in telecommunication and electronic computing. Optionally, reducing D f  relative to E-glass is also desired by the electronic industry. While the PCB industry has a need for low dielectric fiber glass, manufacture of glass fiber reinforcement requires economical viability issues to be addressed in order for low dielectric fibers to achieve successful commercialization. To this end, some low D k  glass compositions proposed in the prior art do not adequately address the economic issues. 
         [0007]    Some low dielectric glasses in the prior art are characterized by high SiO 2  content or high B 2 O 3  content, or a combination of both high SiO 2  and high B 2 O 3 . An example of the latter is known as “D-glass.” Detailed information on this approach to low D k  glass can be found in an article by L. Navias and R. L. Green, “Dielectric Properties of Glasses at Ultra-High Frequencies and their Relation to Composition,” J. Am. Ceram. Soc., 29, 267-276 (1946), in U.S. Patent Application 2003/0054936 A1 (S. Tamura), and in patent application JP 3409806 B2 (Y. Hirokazu). Fibers of SiO 2  and glasses of the D-glass type have been used as reinforcement in fabric form for PCB substrates, e.g., laminates comprised of woven fibers and epoxy resin. Although both of those approaches successfully provide low D k , sometimes as low as about 3.8 or 4.3, the high melting and forming temperatures of such compositions result in undesirably high costs for such fibers. D-glass fibers typically require forming temperatures in excess of 1400° C., and SiO 2  fibers entail forming temperatures on the order of about 2000° C. Furthermore, D-glass is characterized by high B 2 O 3  content, as much as 20 weight percent or greater. Since B 2 O 3  is one of the most costly raw materials required for manufacturing conventional electronic E-glass, the use of much greater amounts of B 2 O 3  in D-glass significantly increases its cost compared to E-glass. Therefore, neither SiO 2  nor D-glass fibers provide a practical solution for manufacturing high performance PCB substrate materials on a large scale. 
         [0008]    Other low dielectric fiber glasses based on high B 2 O 3  concentrations (i.e., 11 to 25 weight percent) plus other relatively costly ingredients such as ZnO (up to 10 weight percent) and BaO (up to 10 weight percent) have been described in JP 3409806B2 (Hirokazu), with reported D k  values in the 4.8-5.6 range at 1 MHz. The inclusion of BaO in these compositions is problematic because of cost as well as environmental reasons. In spite of the high concentrations of the costly B 2 O 3  in the compositions of this reference, the fiber forming temperatures disclosed are relatively high, e.g., 1355° C.-1429° C. Similarly, other low dielectric glasses based on high B 2 O 3  concentrations (i.e., 14-20 weight percent) plus relatively costly TiO 2  (up to 5 weight percent) have been described in U.S. Patent Application 2003/0054936 A1 (Tamura), with D k =4.6-4.8 and dissipation factor D f =0.0007-0.001 at 1 MHz. In Japanese Patent Application JP 02154843A (Hiroshi et al.) there are disclosed boron-free low dielectric glasses with D k  in the range 5.2-5.3 at 1 MHz. Although these boron-free glasses provide low D k  with presumably relatively low raw material cost, their disadvantage is that fiber forming temperatures at 1000 poise melt viscosity are high, between 1376° C. and 1548° C. Additionally, these boron-free glasses have very narrow forming windows (the difference between the forming temperature and the liquidus temperature), typically 25° C. or lower (in some cases negative), whereas a window of about 55° C. or higher would commonly be considered expedient in the commercial fiber glass industry. 
         [0009]    To improve PCB performance while managing the increase in cost, it would be advantageous to provide compositions for fiber glasses that offer significant improvements of electrical properties (D k  and/or D f ) relative to E-glass compositions, and at the same time provide practical forming temperatures lower than the SiO 2  and D-glass types and the other prior art approaches to low dielectric glass discussed above. To significantly lower raw material costs, it would be desirable to maintain B 2 O 3  content less than that of D-glass, e.g., below 13 weight percent or below 12 percent. It can also be advantageous in some situations for the glass composition to fall within the ASTM definition of electronic E-glass, and thus to require no more than 10 weight percent B 2 O 3 . It would also be advantageous to manufacture low D k  glass fibers without requiring costly materials such as BaO or ZnO that are unconventional in the fiber glass industry. In addition, commercially practical glass compositions desirably have tolerance to impurities in raw materials, which also permits the use of less costly batch materials. 
         [0010]    Since an important function of glass fiber in PCB composites is to provide mechanical strength, improvements in electrical properties would best be achieved without significantly sacrificing glass fiber strength. Glass fiber strength can be expressed in terms of Young&#39;s modulus or pristine tensile strength. It would also be desirable if new low dielectric fiber glass solutions would be used to make PCB without requiring major changes in the resins used, or at least without requiring substantially more costly resins, as would be required by some alternative approaches. 
         [0011]    In some embodiments, glass compositions of the present invention are adapted for formation into fibers that can be used in the reinforcement of other polymeric resins in a variety of other end-use applications including, without limitation, aerospace, aviation, wind energy, laminates, radome, and other applications. In such applications, electrical properties, such as those discussed above, may or may not be important. In some applications, other properties, such as specific strength or specific modulus or weight, may be important. In some embodiments, the glass fibers may be first arranged into a fabric. In some embodiments, glass fibers of the present invention can be provided in other forms including, for example and without limitation, as chopped strands (dry or wet), yarns, wovings, prepregs, etc. In short, various embodiments of the glass compositions (and any fibers formed therefrom) can be used in a variety of applications. 
       SUMMARY 
       [0012]    Embodiments of the present invention relate generally to glass compositions and to glass fibers formed from glass compositions. In some embodiments, glass fibers can be used in a number of applications including electrical applications (e.g., printed circuit boards) and reinforcement applications (e.g., fiber glass reinforced composites that can be used in a variety of applications). In some embodiments, fiberizable glass compositions of the present invention can provide improved electrical performance (i.e., low D k  and/or low D f ) relative to standard E-glass, while providing temperature-viscosity relationships that are more conducive to commercially practical fiber forming than prior art low D k  glass proposals. Some embodiments of glass compositions or glass fibers of the present invention can be made commercially with relatively low raw material batch cost. In some embodiments, glass fibers of the present invention can provide desirable and/or commercially acceptable mechanical properties. 
         [0013]    In another aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  53.5-77 weight percent;   B 2 O 3  4.5-14.5 weight percent;   Al 2 O 3  4.5-18.5 weight percent;   MgO 4-12.5 weight percent;   CaO 0-10.5 weight percent;   Li 2 O 0-4 weight percent;   Na 2 O 0-2 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-2 weight percent;   TiO 2  0-2 weight percent; and   other constituents 0-5 weight percent total.       
 
         [0026]    In another aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  60-77 weight percent;   B 2 O 3  4.5-14.5 weight percent;   Al 2 O 3  4.5-18.5 weight percent;   MgO 8-12.5 weight percent;   CaO 0-4 weight percent;   Li 2 O 0-3 weight percent;   Na 2 O 0-2 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-2 weight percent;   TiO 2  0-2 weight percent; and other constituents 0-5 weight percent total.       
 
         [0038]    In one aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  60-68 weight percent;   B 2 O 3  7-13 weight percent;   Al 2 O 3  9-15 weight percent;   MgO 8-15 weight percent;   CaO 0-4 weight percent;   Li 2 O 0-2 weight percent;   Na 2 O 0-1 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-1 weight percent; and   TiO 2  0-2 weight percent.       
 
         [0050]    In another aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  at least 60 weight percent;   B 2 O 3  5-11 weight percent;   Al 2 O 3  5-18 weight percent;   MgO 5-12 weight percent;   CaO 0-10 weight percent;   Li 2 O 0-3 weight percent;   Na 2 O 0-2 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-2 weight percent;   TiO 2  0-2 weight percent; and   other constituents 0-5 weight percent total.       
 
         [0063]    In another aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  60-68 weight percent;   B 2 O 3  5-10 weight percent;   Al 2 O 3  10-18 weight percent;   MgO 8-12 weight percent;   CaO 0-4 weight percent;   Li 2 O 0-3 weight percent;   Na 2 O 0-2 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-2 weight percent;   TiO 2  0-2 weight percent; and   other constituents 0-5 weight percent total.       
 
         [0076]    In another aspect of the invention, glass compositions can comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  62-68 weight percent;   B 2 O 3  7-9 weight percent;   Al 2 O 3  11-18 weight percent;   MgO 8-11 weight percent;   CaO 1-2 weight percent;   Li 2 O 1-2 weight percent;   Na 2 O 0-0.5 weight percent;   K 2 O 0-0.5 weight percent;   Fe 2 O 3  0-0.5 weight percent;   F 2  0.5-1 weight percent;   TiO 2  0-1 weight percent; and   other constituents 0-5 weight percent total.       
 
         [0089]    In some embodiments, the compositions of the invention are characterized by relatively low content of CaO, for example, on the order of about 0-4 weight percent. In yet other embodiments, the CaO content can be on the order of about 0-3 weight percent. In yet other embodiments, the CaO content can be on the order of about 0-2 weight percent. In general, minimizing the CaO content yields improvements in electrical properties, and the CaO content has been reduced to such low levels in some embodiments that it can be considered an optional constituent. In some other embodiments, the CaO content can be on the order of about 1-2 weight percent. 
         [0090]    On the other hand, the MgO content is relatively high for glasses of this type, wherein in some embodiments the MgO content is double that of the CaO content (on a weight percent basis). Some embodiments of the invention can have MgO content greater than about 5.0 weight percent, and in other embodiments the MgO content can be greater than 8.0 weight percent. In some embodiments, the compositions of the invention are characterized by a MgO content, for example, on the order of about 8-13 weight percent. In yet other embodiments, the MgO content can be on the order of about 9-12 weight percent. In some other embodiments, the MgO content can be on the order of about 8-12 weight percent. In yet some other embodiments, the MgO content can be on the order of about 8-10 weight percent. 
         [0091]    In some embodiments, the compositions of the invention are characterized by a (MgO+CaO) content, for example, that is less than 16 weight percent. In yet other embodiments, the (MgO+CaO) content is less than 13 weight percent. In some other embodiments, the (MgO+CaO) content is 7-16 weight percent. In yet some other embodiments, the (MgO+CaO) content can be on the order of about 10-13 weight percent. 
         [0092]    In yet some other embodiments, the compositions of the invention are characterized by a ratio of (MgO+CaO)/(Li 2 O+Na 2 O+K 2 O) content can be on the order of about 9.0. In certain embodiments, the ratio of Li 2 O/(MgO+CaO) content can be on the order of about 0-2.0. In yet some other embodiments, the ratio of Li 2 O/(MgO+CaO) content can be on the order of about 1-2.0. In certain embodiments, the ratio of Li 2 O/(MgO+CaO) content can be on the order of about 1.0. 
         [0093]    In some other embodiments, the (SiO 2 +B 2 O 3 ) content can be on the order of 70-76 weight percent. In yet other embodiments, the (SiO 2 +B 2 O 3 ) content can be on the order of 70 weight percent. In other embodiments, the (SiO 2 +B 2 O 3 ) content can be on the order of 73 weight percent. In still other embodiments, the ratio of the weight percent of Al 2 O 3  to the weigh percent of B 2 O 3  is on the order of 1-3. In some other embodiments, the ratio of the weight percent of Al 2 O 3  to the weigh percent of B 2 O 3  is on the order of 1.5-2.5. In certain embodiments, the SiO 2  content is on the order of 65-68 weight percent. 
         [0094]    As noted above, some low D k  compositions of the prior art have the disadvantage of requiring the inclusion of substantial amounts of BaO, and it can be noted that BaO is not required in the glass compositions of the present invention. Although the advantageous electrical and manufacturing properties of the invention do not preclude the presence of BaO, the absence of deliberate inclusions of BaO can be considered an additional advantage of some embodiments of the present invention. Thus, embodiments of the present invention can be characterized by the presence of less than 1.0 weight percent BaO. In those embodiments in which only trace impurity amounts are present, the BaO content can be characterized as being no more than 0.05 weight percent. 
         [0095]    The compositions of the invention include B 2 O 3  in amounts less that the prior art approaches that rely upon high B 2 O 3  to achieve low D k . This results in significant cost savings. In some embodiments the B 2 O 3  content need be no more than 13 weight percent, or no more than 12 weight percent. Some embodiments of the invention also fall within the ASTM definition of electronic E-glass, i.e., no more than 10 weight percent B 2 O 3 . 
         [0096]    In some embodiments, the compositions of the invention are characterized by a B 2 O 3  content, for example, on the order of about 5-11 weight percent. In some embodiments, the B 2 O 3  content can be 6-11 weight percent. The B 2 O 3  content, in some embodiments, can be 6-9 weight percent. In some embodiments, the B 2 O 3  content can be 5-10 weight percent. In some other embodiments, the B 2 O 3  content is not greater than 9 weight percent. In yet some other embodiments, the B 2 O 3  content is not greater than 8 weight percent. 
         [0097]    In some embodiments, the compositions of the invention are characterized by a Al 2 O 3  content, for example on the order of about 5-18 weight percent. The Al 2 O 3  content, in some embodiments, can be 9-18 weight percent. In yet other embodiments, the Al 2 O 3  content is on the order of about 10-18 weight percent. In some other embodiments, the Al 2 O 3  content is on the order of about 10-16 weight percent. In yet some other embodiments, the Al 2 O 3  content is on the order of about 10-14 weight percent. In certain embodiments, the Al 2 O 3  content is on the order of about 11-14 weight percent. 
         [0098]    In some embodiments, Li 2 O is an optional constituent. In some embodiments, the compositions of the invention are characterized by a Li 2 O content, for example on the order of about 0.4-2.0 weight percent. In some embodiments, the Li 2 O content is greater than the (Na 2 O+K 2 O) content. In some embodiments, the (Li 2 O+Na 2 O+K 2 O) content is not greater than 2 weight percent. In some embodiments, the (Li 2 O+Na 2 O+K 2 O) content is on the order of about 1-2 weight percent. 
         [0099]    In certain embodiments, the compositions of the invention are characterized by a TiO 2  content for example on the order of about 0-1 weight percent. 
         [0100]    In the composition set forth above, the constituents are proportioned so as to yield a glass having a dielectric constant lower than that of standard E-glass. With reference to a standard electronic E-glass for comparison, this may be less than about 6.7 at 1 MHz frequency. In other embodiments, the dielectric constant (D k ) may be less than 6 at 1 MHz frequency. In other embodiments, the dielectric constant (D k ) may be less than 5.8 at 1 MHz frequency. Further embodiments exhibit dielectric constants (D k ) less than 5.6 or even lower at 1 MHz frequency. In other embodiments, the dielectric constant (D k ) may be less than 5.4 at 1 MHz frequency. In yet other embodiments, the dielectric constant (D k ) may be less than 5.2 at 1 MHz frequency. In yet other embodiments, the dielectric constant (D k ) may be less than 5.0 at 1 MHz frequency. 
         [0101]    The compositions set forth above possess desirable temperature-viscosity relationships conducive to practical commercial manufacture of glass fibers. In general, lower temperatures are required for making fibers compared to the D-glass type of composition in the prior art. The desirable characteristics may be expressed in a number of ways, and they may be attained by the compositions of the present invention singly or in combination. In general, glass compositions within the ranges set forth above can be made that exhibit forming temperatures (T F ) at 1000 poise viscosity no greater than 1370° C. The T F  of some embodiments are no greater than 1320° C., or no greater than 1300° C., or no greater than 1290° C., or no greater than 1260° C., or no greater than 1250° C. These compositions also encompass glasses in which the difference between the forming temperature and the liquidus temperature (T L ) is positive, and in some embodiments the forming temperature is at least 55° C. greater than the liquidus temperature, which is advantageous for commercial manufacturing of fibers from these glass compositions. 
         [0102]    In general, minimizing alkali oxide content of the glass compositions assists lowering D k . In those embodiments in which it is desired to optimize reduction of D k  the total alkali oxide content is no more than 2 weight percent of the glass composition. In compositions of the present invention it has been found that minimizing Na 2 O and K 2 O are more effective in this regard than Li 2 O. The presence of alkali oxides generally results in lower forming temperatures. Therefore, in those embodiments of the invention in which providing relatively low forming temperatures is a priority, Li 2 O is included in significant amounts, e.g. at least 0.4 weight percent. For this purpose, in some embodiments the Li 2 O content is greater than either the Na 2 O or K 2 O contents, and in other embodiments the Li 2 O content is greater than the sum of the Na 2 O and K 2 O contents, in some embodiments greater by a factor of two or more. 
         [0103]    In some embodiments, glass compositions suitable for fiber forming may comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  62-68 weight percent;   B 2 O 3  less than about 9 weight percent;   Al 2 O 3  10-18 weight percent;   MgO 8-12 weight percent; and   CaO 0-4 weight percent;
 
wherein the glass exhibits a dielectric constant (D k ) less than 6.7 and a forming temperature (T F ) at 1000 poise viscosity no greater than 1370° C.
       
 
         [0109]    In some embodiments of the invention, the glass compositions may comprise the following constituents, which may be in the form of glass fibers:
       B 2 O 3  less than 14 weight percent;   Al 2 O 3  9-15 weight percent;   MgO 8-15 weight percent;   CaO 0-4 weight percent; and   SiO 2  60-68 weight percent;
 
wherein the glass exhibits a dielectric constant (D k ) less than 6.7 and forming temperature (T F ) at 1000 poise viscosity no greater than 1370° C.
       
 
         [0115]    In some other embodiments of the invention, the glass compositions may comprise the following constituents, which may be in the form of glass fibers:
       B 2 O 3  less than 9 weight percent;   Al 2 O 3  11-18 weight percent;   MgO 8-11 weight percent;   CaO 1-2 weight percent; and   SiO 2  62-68 weight percent;
 
wherein the glass exhibits a dielectric constant (D k ) less than 6.7 and forming temperature (T F ) at 1000 poise viscosity no greater than 1370° C.
       
 
         [0121]    In certain embodiments of the invention, the glass compositions may comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  60-68 weight percent;   B 2 O 3  7-13 weight percent;   Al 2 O 3  9-15 weight percent;   MgO 8-15 weight percent;   CaO 0-3 weight percent;   Li 2 O 0.4-2 weight percent;   Na 2 O 0-1 weight percent;   K 2 O 0-1 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-1 weight percent; and   TiO 2  0-2 weight percent;
 
wherein the glass exhibits a dielectric constant (D k ) less than 5.9 and forming temperature (T F ) at 1000 poise viscosity no greater than 1300° C.
       
 
         [0133]    In some embodiments of the invention, the glass compositions comprise the following constituents, which may be in the form of glass fibers:
       SiO 2  60-68 weight percent;   B 2 O 3  7-11 weight percent;   Al 2 O 3  9-13 weight percent;   MgO 8-13 weight percent;   CaO 0-3 weight percent;   Li 2 O 0.4-2 weight percent;   Na 2 O 0-1 weight percent;   K 2 O 0-1 weight percent;   (Na 2 O+K 2 O+Li 2 O) 0-2 weight percent;   Fe 2 O 3  0-1 weight percent;   F 2  0-1 weight percent; and   TiO 2  0-2 weight percent.       
 
         [0146]    In addition to or instead of the features of the invention described above, some embodiments of the compositions of the present invention can be utilized to provide glasses having dissipation factors (D f ) lower than standard electronic E-glass. In some embodiments, D F  may be no more than 0.0150 at 1 GHz, and in other embodiments no more than 0.0100 at 1 GHz. 
         [0147]    In some embodiments of glass compositions, D F  is no more than 0.007 at 1 GHz, and in other embodiments no more than 0.003 at 1 GHz, and in yet other embodiments no more than 0.002 at 1 GHz. 
         [0148]    One advantageous aspect of the invention present in some of the embodiments is reliance upon constituents that are conventional in the fiber glass industry and avoidance of substantial amounts of constituents whose raw material sources are costly. For this aspect of the invention, constituents in addition to those explicitly set forth in the compositional definition of the glasses of the present invention may be included even though not required, but in total amounts no greater than 5 weight percent. These optional constituents include melting aids, fining aids, colorants, trace impurities and other additives known to those of skill in glassmaking. Relative to some prior art low D k  glasses, no BaO is required in the compositions of the present invention, but inclusion of minor amounts of BaO (e.g., up to about 1 weight percent) would not be precluded. Likewise, major amounts of ZnO are not required in the present invention, but in some embodiments minor amounts (e.g., up to about 2.0 weight percent) may be included. In those embodiments of the invention in which optional constituents are minimized, the total of optional constituents is no more than 2 weight percent, or no more than 1 weight percent. Alternatively, some embodiments of the invention can be said to consist essentially of the named constituents. 
     
    
     DETAILED DESCRIPTION 
       [0149]    To lower D k  and D f , including SiO 2  and B 2 O 3 , which have low electrical polarizability, is useful in the compositions of the present invention. Although B 2 O 3  by itself can be melted at a low temperature (350° C.), it is not stable against moisture attack in ambient air and hence, a fiber of pure B 2 O 3  is not practical for use in PCB laminates. Both SiO 2  and B 2 O 3  are network formers, and the mixture of two would result in significantly higher fiber forming temperature than E-glass, as is the case with D-glass. To lower fiber-forming temperature, MgO and Al 2 O 3  are included, replacing some of the SiO 2 . Calcium oxide (CaO) and SrO can be also used in combination with MgO, although they are less desirable than MgO because both have higher polarizability than MgO. 
         [0150]    To lower batch cost, B 2 O 3  is utilized at lower concentrations than in D-glass. However, sufficient B 2 O 3  is included to prevent phase separation in glass melts, thereby providing better mechanical properties for glass fibers made from the compositions. 
         [0151]    The choice of batch ingredients and their cost are significantly dependent upon their purity requirements. Typical commercial ingredients, such as for E-glass making, contain impurities of Na 2 O, K 2 O, Fe 2 O 3  or FeO, SrO, F 2 , TiO 2 , SO 3 , etc. in various chemical forms. A majority of the cations from these impurities would increase the D k  of the glasses by forming nonbridging oxygens with SiO 2  and/or B 2 O 3  in the glass. 
         [0152]    Sulfate (expressed as SO 3 ) may also be present as a refining agent. Small amounts of impurities may also be present from raw materials or from contamination during the melting processes, such as SrO, BaO, Cl 2 , P 2 O 5 , Cr 2 O 3 , or NiO (not limited to these particular chemical forms). Other refining agents and/or processing aids may also be present such as As 2 O 3 , MnO, MnO 2 , Sb 2 O 3 , or SnO 2 , (not limited to these particular chemical forms). These impurities and refining agents, when present, are each typically present in amounts less than 0.5% by weight of the total glass composition. Optionally, elements from rare earth group of the Periodic Table of the Elements may be added to compositions of the present invention, including atomic numbers 21 (Sc), 39 (Y), and 57 (La) through 71 (Lu). These may serve as either processing aids or to improve the electrical, physical (thermal and optical), mechanical, and chemical properties of the glasses. The rare earth additives may be included with regard for the original chemical forms and oxidization states. Adding rare earth elements is considered optional, particularly in those embodiments of the present invention having the objective of minimizing raw material cost, because they would increase batch costs even at low concentrations. In any case, their costs would typically dictate that the rare earth components (measured as oxides), when included, be present in amounts no greater than about 0.1-1.0% by weight of the total glass composition. 
         [0153]    The invention will be illustrated through the following series of specific embodiments. However, it will be understood by one of skill in the art that many other embodiments are contemplated by the principles of the invention. 
         [0154]    The glasses in these examples were made by melting mixtures of reagent grade chemicals in powder form in 10% Rh/Pt crucibles at the temperatures between 1500° C. and 1550° C. (2732° F.-2822° F.) for four hours. Each batch was about 1200 grams. After the 4-hour melting period, the molten glass was poured onto a steel plate for quenching. To compensate volatility loss of B 2 O 3  (typically about 5% of the total target B 2 O 3  concentration in laboratory batch melting condition for the 1200 gram batch size), the boron retention factor in the batch calculation was set at 95%. Other volatile species, such as fluoride and alkali oxides, were not adjusted in the batches for their emission loss because of their low concentrations in the glasses. The compositions in the examples represent as-batched compositions. Since reagent chemicals were used in preparing the glasses with an adequate adjustment of B 2 O 3 , the as-batched compositions illustrated in the invention are considered to be close to the measured compositions. 
         [0155]    Melt viscosity as a function of temperature and liquidus temperature were determined by using ASTM Test Method C965 “Standard Practice for Measuring Viscosity of Glass Above the Softening Point,” and C829 “Standard Practices for Measurement of Liquidus Temperature of Glass by the Gradient Furnace Method,” respectively. 
         [0156]    A polished disk of each glass sample with 40 mm diameter and 1-1.5 mm thickness was used for electrical property and mechanical property measurements, which were made from annealed glasses. Dielectric constant (D k ) and dissipation factor (D f ) of each glass were determined from 1 MHz to 1 GHz by ASTM Test Method D150 “Standard Test Methods for A-C Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials.” According to the procedure, all samples were preconditioned at 25° C. under 50% humidity for 40 hours. Selective tests were performed for glass density using ASTM Test Method C729 “Standard Test Method for Density of Glass by the Sink-Float Comparator,” for which all samples were annealed. 
         [0157]    For selected compositions, a microindentation method was used to determine Young&#39;s modulus (from the initial slope of the curve of indentation loading—indentation depth, in the indenter unloading cycle), and microhardness (from the maximum indentation load and the maximum indentation depth). For the tests, the same disk samples, which had been tested for D k  and D f , were used. Five indentation measurements were made to obtain average Young&#39;s modulus and microhardness data. The microindentation apparatus was calibrated using a commercial standard reference glass block with a product name BK7. The reference glass has Young&#39;s modulus 90.1 GPa with one standard deviation of 0.26 GPa and microhardness 4.1 GPa with one standard deviation of 0.02 GPa, all of which were based on five measurements. 
         [0158]    All compositional values in the examples are expressed in weight percent. 
       Table 1 Compositions 
       [0159]    Examples 1-8 provide glass compositions (Table 1) by weight percentage: SiO 2  62.5-67.5%, B 2 O 3  8.4-9.4%, Al 2 O 3  10.3-16.0%, MgO 6.5-11.1%, CaO 1.5-5.2%, Li 2 O 1.0%, Na 2 O 0.0%, K 2 O 0.8%, Fe 2 O 3  0.2-0.8%, F 2  0.0%, TiO 2  0.0%, and sulfate (expressed as SO 3 ) 0.0%. 
         [0160]    The glasses were found to have D k  of 5.44-5.67 and Df of 0.0006-0.0031 at 1 MHz, and D k  of 5.47-6.67 and D f  of 0.0048-0.0077 at 1 GHz frequency. The electric properties of the compositions in Series III illustrate significantly lower (i.e., improved) D k  and D f  over standard E-glass with D k  of 7.29 and D f  of 0.003 at 1 MHz and D k  of 7.14 and D f  of 0.0168 at 1 GHz. 
         [0161]    In terms of fiber forming properties, the compositions in Table 1 have forming temperatures (T F ) of 1300-1372° C. and forming windows (T F -T L ) of 89-222° C. This can be compared to a standard E-glass which has T F  typically in the range 1170-1215° C. To prevent glass devitrification in fiber forming, a forming window (T F -T L ) greater than 55° C. is desirable. All of the compositions in Table 1 exhibit satisfactory forming windows. Although the compositions of Table 1 have higher forming temperatures than E-glass, they have significantly lower forming temperatures than D-glass (typically about 1410° C.). 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Al 2 O 3   
                 11.02 
                 9.45 
                 11.64 
                 12.71 
                 15.95 
                 10.38 
                 10.37 
                 11.21 
               
               
                 B 2 O 3   
                 8.55 
                 8.64 
                 8.58 
                 8.56 
                 8.46 
                 8.71 
                 9.87 
                 9.28 
               
               
                 CaO 
                 5.10 
                 5.15 
                 3.27 
                 2.48 
                 1.50 
                 2.95 
                 2.01 
                 1.54 
               
               
                 CoO 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.62 
               
               
                 Fe 2 O 3   
                 0.39 
                 0.40 
                 0.39 
                 0.39 
                 0.39 
                 0.53 
                 0.80 
                 0.27 
               
               
                 K 2 O 
                 0.77 
                 0.78 
                 0.77 
                 0.77 
                 0.76 
                 0.79 
                 0.79 
                 0.78 
               
               
                 Li 2 O 
                 0.98 
                 0.99 
                 0.98 
                 0.98 
                 0.97 
                 1.00 
                 1.00 
                 1.00 
               
               
                 MgO 
                 6.70 
                 7.44 
                 8.04 
                 8.69 
                 9.24 
                 10.39 
                 11.05 
                 11.04 
               
               
                 SiO 2   
                 66.48 
                 67.16 
                 66.32 
                 65.42 
                 62.72 
                 65.26 
                 64.12 
                 64.26 
               
             
          
           
               
                 Properties 
               
             
          
           
               
                 D k , 1 MHz 
                 5.62 
                 5.59 
                 5.44 
                 5.47 
                 5.50 
                 5.67 
                 5.57 
                 5.50 
               
               
                 D k , 1 GHz 
                 5.65 
                 5.62 
                 5.46 
                 5.47 
                 5.53 
                 5.67 
                 5.56 
                 5.50 
               
               
                 D f , 1 MHz 
                 0.0010 
                 0.0006 
                 0.0016 
                 0.0008 
                 0.0020 
                 0.0031 
                 0.0012 
                 0.0010 
               
               
                 D f , 1 GHz 
                 0.0048 
                 0.0059 
                 0.0055 
                 0.0051 
                 0.0077 
                 0.0051 
                 0.0053 
                 0.0049 
               
               
                 T L  (° C.) 
                 1209 
                 1228 
                 1215 
                 1180 
                 1143 
                 1219 
                 1211 
                 1213 
               
               
                 T F  (° C.) 
                 1370 
                 1353 
                 1360 
                 1372 
                 1365 
                 1319 
                 1300 
                 1316 
               
               
                 T F  − T L  (° C.) 
                 161 
                 125 
                 145 
                 192 
                 222 
                 100 
                 89 
                 103 
               
               
                   
               
             
          
         
       
     
       Table 2 Compositions 
       [0162]    Examples 9-15 provide glass compositions: SiO 2  60.8-68.0%, B 2 O 3  8.6 and 11.0%, Al 2 O 3  8.7-12.2%, MgO 9.5-12.5%, CaO 1.0-3.0%, Li 2 O 0.5-1.5%, Na 2 O 0.5%, K 2 O 0.8%, Fe 2 O 3  0.4%, F 2  0.3%, TiO 2  0.2%, and sulfate (expressed as SO 3 ) 0.0%. 
         [0163]    The glasses were found to have D k  of 5.55-5.95 and D f  of 0.0002-0.0013 at 1 MHz, and D k  of 5.54-5.94 and D f  of 0.0040-0.0058 at 1 GHz frequency. The electric properties of the compositions in Table 2 illustrate significantly lower (improved) D k  and D f  over standard E-glass with D k  of 7.29 and D f  of 0.003 at 1 MHz, and D k  of 7.14 and D f  of 0.0168 at 1 GHz. 
         [0164]    In terms of mechanical properties, the compositions of Table 2 have Young&#39;s modulus of 86.5-91.5 GPa and microhardness of 4.0-4.2 GPa, both of which are equal or higher than standard E glass that has Young&#39;s modulus of 85.9 GPa and microhardness of 3.8 GPa. The Young&#39;s moduli of the compositions in the Table 2 are also significantly higher than D-glass which is about 55 GPa based on literature data. 
         [0165]    In terms of fiber forming properties, the compositions of Table 2 have forming temperature (T F ) of 1224-1365° C., and forming windows (T F -T L ) of 6-105° C. as compared to standard E-glass having T F  in the range 1170-1215° C. Some, but not all, of the Table 2 compositions have a forming window (T F -T L ) greater than 55° C., which is considered preferable in some circumstances to avoid glass devitrification in commercial fiber forming operations. The Table 2 compositions have lower forming temperatures than those of D-glass (1410° C.), although higher than E-glass. 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 EXAMPLE: 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Al 2 O 3   
                 12.02 
                 11.88 
                 10.41 
                 12.08 
                 12.18 
                 8.76 
                 12.04 
               
               
                 B 2 O 3   
                 10.98 
                 10.86 
                 9.90 
                 8.71 
                 8.79 
                 8.79 
                 8.68 
               
               
                 CaO 
                 1.07 
                 2.90 
                 2.02 
                 2.95 
                 1.09 
                 1.09 
                 2.94 
               
               
                 F 2   
                 0.32 
                 0.31 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
                 0.32 
               
               
                 Fe 2 O 3   
                 0.40 
                 0.39 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
                 0.40 
               
               
                 K 2 O 
                 0.78 
                 0.77 
                 0.79 
                 0.79 
                 0.79 
                 0.79 
                 0.78 
               
               
                 Li 2 O 
                 0.50 
                 0.49 
                 1.00 
                 0.50 
                 1.51 
                 1.51 
                 1.49 
               
               
                 MgO 
                 12.35 
                 9.56 
                 11.10 
                 12.41 
                 12.51 
                 9.81 
                 9.69 
               
               
                 Na 2 O 
                 0.51 
                 0.51 
                 0.52 
                 0.52 
                 0.52 
                 0.52 
                 0.52 
               
               
                 SiO 2   
                 60.87 
                 62.13 
                 63.35 
                 61.14 
                 61.68 
                 67.80 
                 62.95 
               
               
                 TiO 2   
                 0.20 
                 0.20 
                 0.20 
                 0.20 
                 0.20 
                 0.20 
                 0.20 
               
             
          
           
               
                 Properties 
               
             
          
           
               
                 D k , 1 MHz 
                 5.69 
                 5.55 
                 5.74 
                 5.84 
                 5.95 
                 5.60 
                 5.88 
               
               
                 D k , 1 GHz 
                 5.65 
                 5.54 
                 5.71 
                 5.83 
                 5.94 
                 5.55 
                 5.86 
               
               
                 D f , 1 MHz 
                 0.0007 
                 0.0013 
                 0.0007 
                 0.0006 
                 0.0002 
                 0.0002 
                 0.0011 
               
               
                 D f , 1 GHz 
                 0.0042 
                 0.0040 
                 0.0058 
                 0.0043 
                 0.0048 
                 0.0045 
                 0.0053 
               
               
                 T L  (° C.) 
                 1214 
                 1209 
                 1232 
                 1246 
                 1248 
                 1263 
                 1215 
               
               
                 T F  (° C.) 
                 1288 
                 1314 
                 1287 
                 1277 
                 1254 
                 1365 
                 1285 
               
               
                 T F  − T L  (° C.) 
                 74 
                 105 
                 55 
                 31 
                 6 
                 102 
                 70 
               
               
                 E (GPa) 
                 90.5 
                 87.4 
                 86.8 
                 86.5 
                 89.6 
                 87.2 
                 91.5 
               
               
                 H (GPa) 
                 4.12 
                 4.02 
                 4.02 
                 4.03 
                 4.14 
                 4.07 
                 4.19 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 EXAMPLES: 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
               
                 Al 2 O 3   
                 10.37 
                 11.58 
                 8.41 
                 11.58 
                 12.05 
               
               
                 B 2 O 3   
                 8.71 
                 10.93 
                 10.66 
                 8.98 
                 8.69 
               
               
                 CaO 
                 2.01 
                 2.63 
                 3.02 
                 1.78 
                 2.12 
               
               
                 F 2   
                 0.32 
                 0.30 
                 0.30 
                 0.30 
                 0.30 
               
               
                 Fe 2 O 3   
                 0.40 
                 0.27 
                 0.27 
                 0.27 
                 0.27 
               
               
                 K 2 O 
                 0.79 
                 0.25 
                 0.25 
                 0.16 
                 0.10 
               
               
                 Li 2 O 
                 0.50 
                 1.21 
                 1.53 
                 0.59 
                 1.40 
               
               
                 MgO 
                 11.06 
                 10.04 
                 9.65 
                 11.65 
                 10.57 
               
               
                 Na 2 O 
                 0.52 
                 0.25 
                 0.57 
                 0.35 
                 0.15 
               
               
                 SiO 2   
                 65.13 
                 62.55 
                 65.35 
                 64.35 
                 64.35 
               
               
                 TiO 2   
                 0.20 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                 D k , 1 MHz 
                 5.43 
                 5.57 
                   
                 5.30 
                 5.42 
               
               
                 D k , 1 GHz 
                 5.33 
                 5.48 
                   
                 5.22 
                 5.33 
               
               
                 D f , 1 MHz 
                 0.0057 
                 0.0033 
                   
                 0.0031 
                 0.0051 
               
               
                 D f , 1 GHz 
                 0.0003 
                 0.0001 
                   
                 0.0008 
                 0.0014 
               
               
                 T L  (° C.) 
                 1231 
                 1161 
                 1196 
                 1254 
                 1193 
               
               
                 T F  (° C.) 
                 1327 
                 1262 
                 1254 
                 1312 
                 1299 
               
               
                 T F  − T L  (° C.) 
                 96 
                 101 
                 58 
                 58 
                 106 
               
               
                 T M  (° C.) 
                 1703 
                 1592 
                 1641 
                 1634 
                 1633 
               
               
                 E (GPa) 
                 85.3 
                 86.1 
                 85.7 
                 91.8 
                 89.5 
               
               
                 Std E (GPa) 
                 0.4 
                 0.6 
                 2.5 
                 1.7 
                 1.5 
               
               
                 H (GPa) 
                 3.99 
                 4.00 
                 4.03 
                 4.22 
                 4.13 
               
               
                 Std H (GPa) 
                 0.01 
                 0.02 
                 0.09 
                 0.08 
                 0.05 
               
               
                   
               
             
          
           
               
                 EXAMPLES: 
                 21 
                 22 
                 23 
                 24 
                 25 
                 26 
               
               
                   
               
               
                 Al 2 O 3   
                 12.04 
                 12.04 
                 12.04 
                 12.04 
                 12.04 
                 12.54 
               
               
                 B 2 O 3   
                 8.65 
                 8.69 
                 10.73 
                 10.73 
                 11.07 
                 8.73 
               
               
                 CaO 
                 2.06 
                 2.98 
                 2.98 
                 2.98 
                 2.98 
                 2.88 
               
               
                 F 2   
                 0.45 
                 0.45 
                 0.45 
                 0.45 
                 0.45 
                 2.00 
               
               
                 Fe 2 O 3   
                 0.35 
                 0.35 
                 0.35 
                 0.35 
                 0.35 
                 0.35 
               
               
                 K 2 O 
                 0.4 
                 0.4 
                 0.4 
                 0.4 
                 0.4 
                 0.40 
               
               
                 Li 2 O 
                 1.53 
                 1.05 
                 1.05 
                 0.59 
                 0.48 
               
               
                 MgO 
                 10.47 
                 10.62 
                 9.97 
                 11.26 
                 11.26 
                 11.26 
               
               
                 Na 2 O 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.50 
               
               
                 SiO 2   
                 63.05 
                 62.42 
                 61.03 
                 60.2 
                 59.97 
                 61.34 
               
               
                 TiO 2   
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                 0.5 
                   
               
               
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                 D k , 1 MHz 
                 5.75 
                 5.73 
                 5.61 
                 5.64 
                 5.63 
                 5.35 
               
               
                 D k , 1 GHz 
                 5.68 
                 5.61 
                 5.55 
                 5.54 
                 5.49 
                 5.38 
               
               
                 D f , 1 MHz 
                 0.004 
                 0.0058 
                 0.0020 
                 0.0046 
                 0.0040 
                 0.0063 
               
               
                 D f , 1 GHz 
                 0.0021 
                 0.0024 
                 0.0034 
                 0.0019 
                 0.0023 
                 0.0001 
               
               
                 T L  (° C.) 
                 1185 
                 1191 
                 1141 
                 1171 
                 1149 
                 1227 
               
               
                 T F  (° C.) 
                 1256 
                 1258 
                 1244 
                 1246 
                 1249 
                 1301 
               
               
                 T F  − T L  (° C.) 
                 71 
                 67 
                 103 
                 75 
                 100 
               
               
                 T M  (° C.) 
                 1587 
                 1581 
                 1587 
                 1548 
                 1553 
               
               
                 E (GPa) 
               
               
                 Std E (GPa) 
               
               
                 H (GPa) 
               
               
                 Std H (GPa) 
               
               
                 σ f  (KPSI/GPa) 
                   
                   
                 475.7/3.28 
                 520.9/3.59 
                 466.5/3.22 
                 522.0 
               
               
                 Std σ f   
                   
                   
                  37.3/0.26 
                  18.3/0.13 
                  41.8/0.29 
                 18.70 
               
               
                 (KPSI/GPa) 
               
               
                 Density (g/cm 3 ) 
                   
                   
                 2.4209* 
                 2.4324* 
                 2.4348* 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 EXAMPLE: 
                 27 
                 28 
                 E-Glass 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Al 2 O 3   
                 12.42 
                 12.57 
                 13.98 
               
               
                   
                 B 2 O 3   
                 9.59 
                 8.59 
                 5.91 
               
               
                   
                 CaO 
                 0.11 
                 0.10 
                 22.95 
               
               
                   
                 F 2   
                 0.35 
                 0.26 
                 0.71 
               
               
                   
                 Fe 2 O 3   
                 0.21 
                 0.21 
                 0.36 
               
               
                   
                 K 2 O 
                 0.18 
                 0.18 
                 0.11 
               
               
                   
                 Li 2 O 
                 0.80 
                 1.01 
                 0 
               
               
                   
                 MgO 
                 10.25 
                 10.41 
                 0.74 
               
               
                   
                 Na 2 O 
                 0.15 
                 0.18 
                 0.89 
               
               
                   
                 SiO 2   
                 65.47 
                 65.96 
                 54.15 
               
               
                   
                 TiO 2   
                 0.17 
                 0.17 
                 0.07 
               
               
                   
                 D k , 1 MHz 
                 5.3 
                 5.4 
                 7.3 
               
               
                   
                 D k , 1 GHz 
                 5.3 
                 5.4 
                 7.1 
               
               
                   
                 D f , 1 MHz 
                 0.003 
                 0.008 
               
               
                   
                 D f , 1 GHz 
                 0.011 
                 0.012 
                 0.0168 
               
               
                   
                 T L  (° C.) 
                 1184 
                 1201 
                 1079 
               
               
                   
                 T F  (° C.) 
                 1269 
                 1282 
                 1173 
               
               
                   
                 T F  − T L  (° C.) 
                 85 
                 81 
                 94 
               
               
                   
                 E (GPa) 
               
               
                   
                 H (GPa) 
                 3.195 
                 3.694 
               
               
                   
                   
               
             
          
         
       
     
         [0166]    Examples 29-62 provide glass compositions (Table 5) by weight percentage: SiO 2  53.74-76.97%, B 2 O 3  4.47-14.28%, Al 2 O 3  4.63-15.44%, MgO 4.20-12.16%, CaO 1.04-10.15%, Li 2 O 0.0-3.2%, Na 2 O 0.0-1.61%, K 2 O 0.01-0.05%, Fe 2 O 3  0.06-0.35%, F 2  0.49-1.48%, TiO 2  0.05-0.65%, and sulfate (expressed as SO 3 ) 0.0-0.16%. 
         [0167]    Examples 29-62 provide glass compositions (Table 5) by weight percentage wherein the (MgO+CaO) content is 7.81-16.00%, the ratio CaO/MgO is 0.09-1.74%, the (SiO 2 +B 2 O 3 ) content is 67.68-81.44%, the ratio Al 2 O 3 /B 2 O 3  is 0.90-1.71%, the (Li 2 O+Na 2 O+K 2 O) content is 0.03-3.38%, and the ratio Li 2 O/(Li 2 O+Na 2 O+K 2 O) is 0.00-0.95%. 
         [0168]    In terms of mechanical properties, the compositions of Table 5 have a fiber density of 2.331-2.416 g/cm 3  and an average fiber tensile strength (or fiber strength) of 3050-3578 MPa. 
         [0169]    To measure fiber tensile strength, fiber samples from the glass compositions were produced from a 10 Rh/90 Pt single tip fiber drawing unit. Approximately, 85 grams of cullet of a given composition was fed into the bushing melting unit and conditioned at a temperature close or equal to the 100 Poise melt viscosity for two hours. The melt was subsequently lowered to a temperature close or equal to the 1000 Poise melt viscosity and stabilized for one hour prior to fiber drawing. Fiber diameter was controlled to produce an approximately 10 μm diameter fiber by controlling the speed of the fiber drawing winder. All fiber samples were captured in air without any contact with foreign objects. The fiber drawing was completed in a room with a controlled humidity of between 40 and 45% RH. 
         [0170]    Fiber tensile strength was measured using a Kawabata KES-G1 (Kato Tech Co. Ltd., Japan) tensile strength analyzer equipped with a Kawabata type C load cell. Fiber samples were mounted on paper framing strips using a resin adhesive. A tensile force was applied to the fiber until failure, from which the fiber strength was determined based on the fiber diameter and breaking stress. The test was done at room temperature under the controlled humidity between 40-45% RH. The average values and standard deviations were computed based on a sample size of 65-72 fibers for each composition. 
         [0171]    The glasses were found to have D k  of 4.83-5.67 and D f  of 0.003-0.007 at 1 GHz. The electric properties of the compositions in Table 5 illustrate significantly lower (i.e., improved) D k  and D f  over standard E-glass which has a D k  of 7.14 and a D f  of 0.0168 at 1 GHz. 
         [0172]    In terms of fiber forming properties, the compositions in Table 5 have forming temperatures (T F ) of 1247-1439° C. and forming windows (T F -T L ) of 53-243° C. The compositions in Table 5 have liquidus temperature (T L ) of 1058-1279° C. This can be compared to a standard E-glass which has T F  typically in the range 1170-1215° C. To prevent glass devitrification in fiber forming, a forming window (T F -T L ) greater than 55° C. is sometimes desirable. All of the compositions in Table 5 exhibit satisfactory forming windows. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
             
             
               
                 wt % 
                 29 
                 30 
                 31 
                 32 
                 33 
               
               
                   
               
               
                 SiO 2   
                 64.24 
                 58.62 
                 57.83 
                 61.00 
                 61.56 
               
               
                 Al 2 O 3   
                 11.54 
                 12.90 
                 12.86 
                 12.87 
                 12.82 
               
               
                 Fe 2 O 3   
                 0.28 
                 0.33 
                 0.33 
                 0.33 
                 0.32 
               
               
                 CaO 
                 1.70 
                 1.04 
                 2.48 
                 2.48 
                 1.08 
               
               
                 MgO 
                 11.69 
                 11.63 
                 12.16 
                 9.31 
                 10.69 
               
               
                 Na 2 O 
                 0.01 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 K 2 O 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
               
               
                 B 2 O 3   
                 8.96 
                 14.28 
                 13.15 
                 12.81 
                 12.30 
               
               
                 F 2   
                 0.53 
                 0.62 
                 0.61 
                 0.61 
                 0.65 
               
               
                 TiO 2   
                 0.40 
                 0.54 
                 0.54 
                 0.54 
                 0.54 
               
               
                 Li 2 O 
                 0.60 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 SO 3   
                 0.01 
                 0.01 
                 0.01 
                 0.01 
                 0.01 
               
               
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                 (MgO + CaO) 
                 13.39 
                 12.67 
                 14.64 
                 11.79 
                 11.77 
               
               
                 CaO/Mg 
                 0.15 
                 0.09 
                 0.20 
                 0.27 
                 0.10 
               
               
                 MgO/(MgO + CaO) 
                 0.87 
                 0.92 
                 0.83 
                 0.79 
                 0.91 
               
               
                 SiO 2  + B 2 O 3   
                 73.20 
                 72.90 
                 70.98 
                 73.81 
                 73.86 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.29 
                 0.90 
                 0.98 
                 1.00 
                 1.04 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 0.64 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.94 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 T L  (° C.) 
                 1196 
                 1228 
                 1205 
                 1180 
                 1249 
               
               
                 T F  (° C.) 
                 1331 
                 1300 
                 1258 
                 1334 
                 1332 
               
               
                 T F  − T L  (° C.) 
                 135 
                 72 
                 53 
                 154 
                 83 
               
               
                 D k  @ 1 GHz 
                 5.26 
                 *** 
                 *** 
                 5.30 
                 *** 
               
               
                 D f  @ 1 GHz 
                 0.0017 
                 *** 
                 *** 
                 0.001 
                 *** 
               
               
                 Fiber density (g/cm 3 ) 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                 Fiber strength (MPa) 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
               
             
          
           
               
                 wt % 
                 34 
                 35 
                 36 
                 37 
                 38 
               
               
                   
               
               
                 SiO 2   
                 63.83 
                 65.21 
                 66.70 
                 60.02 
                 53.74 
               
               
                 Al 2 O 3   
                 10.97 
                 10.56 
                 10.11 
                 12.32 
                 15.44 
               
               
                 Fe 2 O 3   
                 0.26 
                 0.25 
                 0.24 
                 0.29 
                 0.24 
               
               
                 CaO 
                 2.38 
                 2.29 
                 2.19 
                 4.01 
                 3.83 
               
               
                 MgO 
                 10.64 
                 10.23 
                 9.79 
                 9.95 
                 10.53 
               
               
                 Na 2 O 
                 0.29 
                 0.28 
                 0.27 
                 0.33 
                 0.09 
               
               
                 K 2 O 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
               
               
                 B 2 O 3   
                 9.32 
                 8.96 
                 8.57 
                 10.48 
                 13.94 
               
               
                 F 2   
                 1.20 
                 1.16 
                 1.11 
                 1.35 
                 1.48 
               
               
                 TiO 2   
                 0.36 
                 0.35 
                 0.33 
                 0.41 
                 0.65 
               
               
                 Li 2 O 
                 0.70 
                 0.67 
                 0.64 
                 0.79 
                 0.02 
               
               
                 SO 3   
                 0.14 
                 0.14 
                 0.13 
                 0.16 
                 0.14 
               
               
                 Total 
                 100.13 
                 100.13 
                 100.12 
                 100.15 
                 100.13 
               
               
                 (MgO + CaO) 
                 13.02 
                 12.52 
                 11.98 
                 13.96 
                 14.36 
               
               
                 CaO/MgO 
                 0.22 
                 0.22 
                 0.22 
                 0.40 
                 0.36 
               
               
                 MgO/(MgO + CaO) 
                 0.82 
                 0.82 
                 0.82 
                 0.71 
                 0.73 
               
               
                 SiO 2  + B 2 O 3   
                 73.15 
                 74.17 
                 75.27 
                 70.50 
                 67.68 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.18 
                 1.18 
                 1.18 
                 1.18 
                 1.11 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 1.02 
                 0.98 
                 0.94 
                 1.15 
                 0.14 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.69 
                 0.68 
                 0.68 
                 0.69 
                 0.16 
               
               
                 T L  (° C.) 
                 1255 
                 1267 
                 1279 
                 1058 
                 1175 
               
               
                 T F  (° C.) 
                 1313 
                 1320 
                 1333 
                 1266 
                 1247 
               
               
                 T F  − T L  (° C.) 
                 58 
                 53 
                 54 
                 208 
                 72 
               
               
                 D k  @ 1 GHz 
                 *** 
                 5.46 
                 5.43 
                 5.56 
                 5.57 
               
               
                 D f  @ 1 GHz 
                 *** 
                 0.0036 
                 0.0020 
                 0.0025 
                 0.00437 
               
               
                 Fiber density (g/cm 3 ) 
                 2.402 
                 2.408 
                 2.352 
                 2.416 
                 *** 
               
               
                 Fiber strength (MPa) 
                 3310 
                 3354 
                 3369 
                 3413 
                 *** 
               
               
                   
               
               
                 wt % 
                 39 
                 40 
                 41 
                 42 
                 43 
               
               
                   
               
               
                 SiO 2   
                 62.54 
                 63.83 
                 65.21 
                 66.70 
                 59.60 
               
               
                 Al 2 O 3   
                 11.36 
                 10.97 
                 10.56 
                 10.11 
                 13.52 
               
               
                 Fe 2 O 3   
                 0.27 
                 0.26 
                 0.25 
                 0.24 
                 0.33 
               
               
                 CaO 
                 2.47 
                 2.38 
                 2.29 
                 2.19 
                 1.80 
               
               
                 MgO 
                 11.02 
                 10.64 
                 10.23 
                 9.79 
                 9.77 
               
               
                 Na 2 O 
                 0.31 
                 0.29 
                 0.28 
                 0.27 
                 0.10 
               
               
                 K 2 O 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
               
               
                 B 2 O 3   
                 9.65 
                 9.32 
                 8.96 
                 8.57 
                 12.70 
               
               
                 F 2   
                 1.25 
                 1.20 
                 1.16 
                 1.11 
                 1.21 
               
               
                 TiO 2   
                 0.37 
                 0.36 
                 0.35 
                 0.33 
                 0.51 
               
               
                 Li 2 O 
                 0.73 
                 0.70 
                 0.67 
                 0.64 
                 0.41 
               
               
                 SO 3   
                 0.15 
                 0.14 
                 0.14 
                 0.13 
                 0.15 
               
               
                 Total 
                 100.14 
                 100.13 
                 100.13 
                 100.12 
                 100.14 
               
               
                 (MgO + CaO) 
                 13.49 
                 13.02 
                 12.52 
                 11.98 
                 11.57 
               
               
                 CaO/MgO 
                 0.22 
                 0.22 
                 0.22 
                 0.22 
                 0.18 
               
               
                 MgO/(MgO + CaO) 
                 0.82 
                 0.82 
                 0.82 
                 0.82 
                 0.84 
               
               
                 SiO 2  + B 2 O 3   
                 72.19 
                 73.15 
                 74.17 
                 75.27 
                 72.30 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.18 
                 1.18 
                 1.18 
                 1.18 
                 1.06 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 1.07 
                 1.02 
                 0.98 
                 0.94 
                 0.54 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.68 
                 0.69 
                 0.68 
                 0.68 
                 0.76 
               
               
                 T L  (° C.) 
                 1238 
                 1249 
                 1266 
                 1276 
                 1083 
               
               
                 T F  (° C.) 
                 1293 
                 1313 
                 1342 
                 1368 
                 1310 
               
               
                 T F  − T L  (° C.) 
                 55 
                 64 
                 76 
                 92 
                 227 
               
               
                 D k  @ 1 GHz 
                 5.45 
                 5.31 
                 5.39 
                 5.25 
                 5.20 
               
               
                 D f  @ 1 GHz 
                 0.00531 
                 0.00579 
                 0.00525 
                 0.00491 
                 0.00302 
               
               
                 Fiber density (g/cm 3 ) 
                 2.403 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                 Fiber strength (MPa) 
                 3467 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
               
             
          
           
               
                 wt % 
                 44 
                 45 
                 46 
                 47 
                 48 
               
               
                   
               
               
                 SiO 2   
                 59.90 
                 60.45 
                 62.68 
                 65.30 
                 65.06 
               
               
                 Al 2 O 3   
                 13.23 
                 13.06 
                 12.28 
                 11.51 
                 12.58 
               
               
                 Fe 2 O 3   
                 0.34 
                 0.35 
                 0.20 
                 0.19 
                 0.25 
               
               
                 CaO 
                 1.86 
                 1.58 
                 1.65 
                 1.39 
                 1.25 
               
               
                 MgO 
                 10.14 
                 10.50 
                 8.74 
                 8.18 
                 6.56 
               
               
                 Na 2 O 
                 0.10 
                 0.10 
                 0.10 
                 0.09 
                 0.13 
               
               
                 K 2 O 
                 0.03 
                 0.03 
                 0.02 
                 0.02 
                 0.05 
               
               
                 B 2 O 3   
                 12.40 
                 12.29 
                 12.69 
                 11.89 
                 10.03 
               
               
                 F 2   
                 1.26 
                 1.07 
                 1.11 
                 0.94 
                 0.82 
               
               
                 TiO 2   
                 0.53 
                 0.55 
                 0.51 
                 0.48 
                 0.07 
               
               
                 Li 2 O 
                 0.20 
                 0.00 
                 0.00 
                 0.00 
                 3.20 
               
               
                 SO 3   
                 0.15 
                 0.16 
                 0.15 
                 0.14 
                 0.11 
               
               
                 Total 
                 100.14 
                 100.15 
                 100.14 
                 100.13 
                 100.10 
               
               
                 RO (MgO + CaO) 
                 12.00 
                 12.08 
                 10.39 
                 9.57 
                 7.81 
               
               
                 CaO/Mg 
                 0.18 
                 0.15 
                 0.19 
                 0.17 
                 0.19 
               
               
                 MgO/(MgO + CaO) 
                 0.85 
                 0.87 
                 0.84 
                 0.85 
                 0.84 
               
               
                 SiO 2  + B 2 O 3   
                 72.30 
                 72.74 
                 75.37 
                 77.19 
                 75.09 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.07 
                 1.06 
                 0.97 
                 0.97 
                 1.25 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 0.33 
                 0.13 
                 0.12 
                 0.11 
                 3.38 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.61 
                 0.00 
                 0.00 
                 0.00 
                 0.95 
               
               
                 T L  (° C.) 
                 1129 
                 1211 
                 1201 
                 1196 
                 *** 
               
               
                 T F  (° C.) 
                 1303 
                 1378 
                 1378 
                 1439 
                 *** 
               
               
                 T F  − T L  (° C.) 
                 174 
                 167 
                 177 
                 243 
                 *** 
               
               
                 Dk @ 1 GHz 
                 5.24 
                 5.05 
                 4.94 
                 4.83 
                 5.67 
               
               
                 Df @ 1 GHz 
                 0.00473 
                 0.00449 
                 0.00508 
                 0.00254 
                 0.007 
               
               
                 Fiber density (g/cm 3 ) 
                 2.387 
                 2.385 
                 2.354 
                 2.34 
                 2.345 
               
               
                 Fiber strength (MPa) 
                 3483 
                 3362 
                 3166 
                 3050 
                 3578 
               
               
                   
               
             
          
           
               
                 wt % 
                 49 
                 50 
                 51 
                 52 
                 53 
               
               
                   
               
               
                 SiO 2   
                 61.14 
                 60.83 
                 62.45 
                 61.88 
                 66.25 
               
               
                 Al 2 O 3   
                 12.90 
                 13.02 
                 12.52 
                 12.72 
                 10.60 
               
               
                 Fe 2 O 3   
                 0.27 
                 0.28 
                 0.26 
                 0.28 
                 0.18 
               
               
                 CaO 
                 1.72 
                 1.74 
                 1.59 
                 1.63 
                 3.33 
               
               
                 MgO 
                 9.25 
                 9.36 
                 8.98 
                 9.13 
                 5.98 
               
               
                 Na 2 O 
                 0.10 
                 0.10 
                 0.10 
                 0.10 
                 0.86 
               
               
                 K 2 O 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
                 0.02 
               
               
                 B 2 O 3   
                 12.70 
                 12.70 
                 12.29 
                 12.38 
                 11.44 
               
               
                 F 2   
                 1.16 
                 1.17 
                 1.08 
                 1.10 
                 0.90 
               
               
                 TiO 2   
                 0.51 
                 0.51 
                 0.50 
                 0.50 
                 0.44 
               
               
                 Li 2 O 
                 0.21 
                 0.25 
                 0.21 
                 0.25 
                 0.00 
               
               
                 SO 3   
                 0.15 
                 0.15 
                 0.14 
                 0.14 
                 0.00 
               
               
                 Total 
                 100.14 
                 100.14 
                 100.13 
                 100.13 
                 100.00 
               
               
                 (MgO + CaO) 
                 10.97 
                 11.10 
                 10.57 
                 10.76 
                 9.31 
               
               
                 CaO/Mg 
                 0.19 
                 0.19 
                 0.18 
                 0.18 
                 0.56 
               
               
                 MgO/(MgO + CaO) 
                 0.84 
                 0.84 
                 0.85 
                 0.85 
                 0.64 
               
               
                 SiO 2  + B 2 O 3   
                 73.84 
                 73.53 
                 74.74 
                 74.26 
                 77.69 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.02 
                 1.03 
                 1.02 
                 1.03 
                 0.93 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 0.34 
                 0.38 
                 0.34 
                 0.38 
                 0.88 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.62 
                 0.66 
                 0.62 
                 0.66 
                 0.00 
               
               
                 T L  (° C.) 
                 1179 
                 1179 
                 1186 
                 1191 
                 *** 
               
               
                 T F  (° C.) 
                 1342 
                 1340 
                 1374 
                 1366 
                 *** 
               
               
                 T F  − T L  (° C.) 
                 163 
                 161 
                 188 
                 175 
                 *** 
               
               
                 D k  @ 1 GHz 
                 *** 
                 5.24 
                 4.96 
                 5.06 
                 5.03 
               
               
                 D f  @ 1 GHz 
                 *** 
                 0.0018 
                 0.0015 
                 0.0014 
                 0.0027 
               
               
                 Fiber density (g/cm 3 ) 
                 2.358 
                 2.362 
                 2.338 
                 *** 
                 2.331 
               
               
                 Fiber strength (MPa) 
                 3545 
                 3530 
                 3234 
                 *** 
                 3161 
               
               
                   
               
             
          
           
               
                   
                 wt % 
                 54 
                 55 
                 56 
                 57 
                 58 
               
               
                   
                   
               
               
                   
                 SiO 2   
                 66.11 
                 69.19 
                 70.68 
                 69.44 
                 69.40 
               
               
                   
                 Al 2 O 3   
                 10.58 
                 10.37 
                 8.87 
                 7.20 
                 7.21 
               
               
                   
                 Fe 2 O 3   
                 0.18 
                 0.18 
                 0.16 
                 0.13 
                 0.14 
               
               
                   
                 CaO 
                 5.31 
                 5.20 
                 5.50 
                 5.57 
                 10.15 
               
               
                   
                 MgO 
                 4.20 
                 7.13 
                 7.54 
                 10.39 
                 5.85 
               
               
                   
                 Na 2 O 
                 0.86 
                 0.55 
                 0.59 
                 0.59 
                 0.59 
               
               
                   
                 K 2 O 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                   
                 B 2 O 3   
                 11.41 
                 6.39 
                 5.72 
                 5.80 
                 5.79 
               
               
                   
                 F 2   
                 0.90 
                 0.53 
                 0.55 
                 0.55 
                 0.55 
               
               
                   
                 TiO 2   
                 0.44 
                 0.43 
                 0.37 
                 0.30 
                 0.30 
               
               
                   
                 Li 2 O 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 SO 3   
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                   
                 (MgO + CaO) 
                 9.51 
                 12.33 
                 13.04 
                 15.96 
                 16.00 
               
               
                   
                 CaO/Mg 
                 1.26 
                 0.73 
                 0.73 
                 0.54 
                 1.74 
               
               
                   
                 MgO/(MgO + CaO) 
                 0.44 
                 0.58 
                 0.58 
                 0.65 
                 0.37 
               
               
                   
                 SiO 2  + B 2 O 3   
                 77.52 
                 75.58 
                 76.40 
                 75.24 
                 75.19 
               
               
                   
                 Al 2 O 3 /B 2 O 3   
                 0.93 
                 1.62 
                 1.55 
                 1.24 
                 1.25 
               
               
                   
                 (Li 2 O + Na 2 O + K 2 O) 
                 0.88 
                 0.57 
                 0.61 
                 0.61 
                 0.61 
               
               
                   
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 T L  (° C.) 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 T F  (° C.) 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 T F  − T L  (° C.) 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 D k  @ 1 GHz 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 D f  @ 1 GHz 
                 *** 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 Fiber density (g/cm 3 ) 
                 2.341 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 Fiber strength (MPa) 
                 3372 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                   
               
             
          
           
               
                   
                 wt % 
                 59 
                 60 
                 61 
                 62 
               
               
                   
                   
               
               
                   
                 SiO 2   
                 69.26 
                 71.45 
                 74.07 
                 76.97 
               
               
                   
                 Al 2 O 3   
                 8.72 
                 5.30 
                 7.27 
                 4.63 
               
               
                   
                 Fe 2 O 3   
                 0.13 
                 0.06 
                 0.09 
                 0.10 
               
               
                   
                 CaO 
                 4.89 
                 5.24 
                 4.88 
                 5.69 
               
               
                   
                 MgO 
                 9.92 
                 10.63 
                 4.77 
                 5.56 
               
               
                   
                 Na 2 O 
                 0.53 
                 0.58 
                 0.73 
                 1.61 
               
               
                   
                 K 2 O 
                 0.03 
                 0.02 
                 0.03 
                 0.01 
               
               
                   
                 B 2 O 3   
                 5.09 
                 4.96 
                 6.39 
                 4.47 
               
               
                   
                 F 2   
                 0.49 
                 0.50 
                 0.66 
                 0.77 
               
               
                   
                 TiO 2   
                 0.27 
                 0.05 
                 0.17 
                 0.19 
               
               
                   
                 Li 2 O 
                 0.69 
                 1.20 
                 0.95 
                 0.00 
               
               
                   
                 SO 3   
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                   
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                   
                 (MgO + CaO) 
                 14.81 
                 15.87 
                 9.65 
                 11.25 
               
               
                   
                 CaO/Mg 
                 0.49 
                 0.49 
                 1.02 
                 1.02 
               
               
                   
                 MgO/(MgO + CaO) 
                 0.67 
                 0.67 
                 0.49 
                 0.49 
               
               
                   
                 SiO 2  + B 2 O 3   
                 74.35 
                 76.41 
                 80.46 
                 81.44 
               
               
                   
                 Al 2 O 3 /B 2 O 3   
                 1.71 
                 1.07 
                 1.14 
                 1.04 
               
               
                   
                 (Li 2 O + Na 2 O + K 2 O) 
                 1.25 
                 1.80 
                 1.71 
                 1.62 
               
               
                   
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.55 
                 0.67 
                 0.56 
                 0.00 
               
               
                   
                 T L  (° C.) 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 T F  (° C.) 
                 1358/1355 
                 1331/1333 
                 1493/1484 
                 *** 
               
               
                   
                 T F  − T L  (° C.) 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 D k  @ 1 GHz 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 D f  @ 1 GHz 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 Fiber density (g/cm 3 ) 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                 Fiber strength (MPa) 
                 *** 
                 *** 
                 *** 
                 *** 
               
               
                   
                   
               
             
          
         
       
     
         [0173]    Examples 63-73 provide glass compositions (Table 6) by weight percentage: SiO 2  62.35-68.35%, B 2 O 3  6.72-8.67%, Al 2 O 3  10.53-18.04%, MgO 8.14-11.44%, CaO 1.67-2.12%, Li 2 O 1.07-1.38%, Na 2 O 0.02%, K 2 O 0.03-0.04%, Fe 2 O 3  0.23-0.33%, F 2  0.49-0.60%, TiO 2  0.26-0.61%, and sulfate (expressed as SO 3 ) 0.0%. 
         [0174]    Examples 63-73 provide glass compositions (Table 6) by weight percentage wherein the (MgO+CaO) content is 9.81-13.34%, the ratio CaO/MgO is 0.16-0.20, the (SiO 2 +B 2 O 3 ) content is 69.59-76.02%, the ratio Al 2 O 3 /B 2 O 3  is 1.37-2.69, the (Li 2 O+Na 2 O+K 2 O) content is 1.09-1.40%, and the ratio Li 2 O/(Li 2 O+Na 2 O+K 2 O) is 0.98. 
         [0175]    In terms of mechanical properties, the compositions of Table 6 have a fiber density of 2.371-2.407 g/cm 3  and an average fiber tensile strength (or fiber strength) of 3730-4076 MPa. The fiber tensile strengths for the fibers made from the compositions of Table 6 were measured in the same way as the fiber tensile strengths measured in connection with the compositions of Table 5. 
         [0176]    The fibers formed from the compositions were found to have Young&#39;s modulus (E) values ranging from 73.84-81.80 GPa. The Young&#39;s modulus (E) values for the fibers were measured using the sonic modulus method on fibers. Elastic modulus values for the fibers drawn from glass melts having the recited compositions were determined using an ultrasonic acoustic pulse technique on a Panatherm 5010 instrument from Panametrics, Inc. of Waltham, Mass. Extensional wave reflection time was obtained using twenty micro-second duration, 200 kHz pulses. The sample length was measured and the respective extensional wave velocity (V E ) was calculated. Fiber density (p) was measured using a Micromeritics AccuPyc 1330 pycnometer. In general, 20 measurements were made for each composition and the average Young&#39;s modulus (E) was calculated according to the formula E=V E   2 *ρ. The fiber failure strain was calculated using Hooke&#39;s Law based on the known fiber strength and Young&#39;s modulus values. 
         [0177]    The glasses were found to have D k  of 5.20-5.54 and Df of 0.0010-0.0020 at 1 GHz. The electric properties of the compositions in Table 6 illustrate significantly lower (i.e., improved) D k  and D f  over standard E-glass with D k  of 7.14 and D f  of 0.0168 at 1 GHz. 
         [0178]    In terms of fiber forming properties, the compositions in Table 6 have forming temperatures (T F ) of 1303-1388° C. and forming windows (T F -T L ) of 51-144° C. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
               
                   
               
             
             
               
                 wt % 
                 63 
                 64 
                 65 
                 66 
                 67 
               
               
                   
               
               
                 SiO 2   
                 64.25 
                 65.35 
                 66.38 
                 67.35 
                 68.35 
               
               
                 Al 2 O 3   
                 11.88 
                 11.52 
                 11.18 
                 10.86 
                 10.53 
               
               
                 Fe 2 O 3   
                 0.26 
                 0.25 
                 0.24 
                 0.24 
                 0.23 
               
               
                 CaO 
                 2.12 
                 2.05 
                 1.99 
                 1.93 
                 1.87 
               
               
                 MgO 
                 10.50 
                 10.17 
                 9.87 
                 9.58 
                 9.29 
               
               
                 Na 2 O 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                 K 2 O 
                 0.04 
                 0.03 
                 0.03 
                 0.03 
                 0.03 
               
               
                 B 2 O 3   
                 8.67 
                 8.40 
                 8.15 
                 7.91 
                 7.67 
               
               
                 F 2   
                 0.60 
                 0.58 
                 0.56 
                 0.54 
                 0.53 
               
               
                 TiO 2   
                 0.30 
                 0.29 
                 0.28 
                 0.27 
                 0.26 
               
               
                 Li 2 O 
                 1.38 
                 1.33 
                 1.29 
                 1.26 
                 1.22 
               
               
                 SO 3   
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                 (MgO + CaO) 
                 12.61 
                 12.22 
                 11.86 
                 11.51 
                 11.16 
               
               
                 CaO/MgO 
                 0.20 
                 0.20 
                 0.20 
                 0.20 
                 0.20 
               
               
                 MgO/(MgO + CaO) 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
                 0.83 
               
               
                 SiO 2  + B 2 O 3   
                 72.92 
                 73.75 
                 74.53 
                 75.26 
                 76.02 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.37 
                 1.37 
                 1.37 
                 1.37 
                 1.37 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 1.40 
                 1.36 
                 1.32 
                 1.28 
                 1.24 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
               
               
                 T L  (° C.) 
                 1241 
                 1259 
                 1266 
                 1268 
                 1287 
               
               
                 T F  (° C.) 
                 1306 
                 1329 
                 1349 
                 1374 
                 1388 
               
               
                 T F  − T L  (° C.) 
                 65 
                 70 
                 83 
                 106 
                 101 
               
               
                 D k  @ 1 GHz 
                 5.44 
                 5.35 
                 5.29 
                 5.31 
                 5.2 
               
               
                 D f  @ 1 GHz 
                 0.0013 
                 0.0016 
                 0.001 
                 0.002 
                 0.0013 
               
               
                 Fiber density (g/cm 3 ) 
                 2.395 
                 2.385 
                 2.384 
                 2.375 
                 2.371 
               
               
                 Fiber strength (MPa) 
                 3730 
                 3759 
                 3813 
                 3743 
                 3738 
               
               
                 Young&#39;s Modulus (GPa) 
                 *** 
                 *** 
                 *** 
                 74.25 
                 *** 
               
               
                 Fiber failure strain (%) 
                 *** 
                 *** 
                 *** 
                 5.04 
                 *** 
               
               
                   
               
             
          
           
               
                 wt % 
                 68 
                 69 
                 70 
                 71 
                 72 
                 73 
               
               
                   
               
               
                 SiO 2   
                 64.39 
                 63.63 
                 62.87 
                 65.45 
                 65.61 
                 62.35 
               
               
                 Al 2 O 3   
                 14.05 
                 16.04 
                 18.04 
                 11.05 
                 14.29 
                 14.74 
               
               
                 Fe 2 O 3   
                 0.28 
                 0.30 
                 0.33 
                 0.24 
                 0.28 
                 0.29 
               
               
                 CaO 
                 1.90 
                 1.79 
                 1.67 
                 1.91 
                 1.77 
                 1.79 
               
               
                 MgO 
                 9.39 
                 8.77 
                 8.14 
                 11.44 
                 8.72 
                 11.37 
               
               
                 Na 2 O 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
                 0.02 
               
               
                 K 2 O 
                 0.04 
                 0.04 
                 0.04 
                 0.03 
                 0.04 
                 0.04 
               
               
                 B 2 O 3   
                 7.75 
                 7.23 
                 6.72 
                 7.80 
                 7.19 
                 7.28 
               
               
                 F 2   
                 0.54 
                 0.51 
                 0.49 
                 0.54 
                 0.51 
                 0.51 
               
               
                 TiO 2   
                 0.41 
                 0.51 
                 0.61 
                 0.28 
                 0.43 
                 0.45 
               
               
                 Li 2 O 
                 1.23 
                 1.15 
                 1.07 
                 1.24 
                 1.14 
                 1.16 
               
               
                 SO 3   
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Total 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
                 100.00 
               
               
                 (MgO + CaO) 
                 11.29 
                 10.55 
                 9.81 
                 13.34 
                 10.49 
                 13.16 
               
               
                 CaO/MgO 
                 0.20 
                 0.20 
                 0.20 
                 0.17 
                 0.20 
                 0.16 
               
               
                 MgO/(MgO + CaO) 
                 0.83 
                 0.83 
                 0.83 
                 0.86 
                 0.83 
                 0.86 
               
               
                 SiO 2  + B 2 O 3   
                 72.14 
                 70.87 
                 69.59 
                 73.25 
                 72.80 
                 69.63 
               
               
                 Al 2 O 3 /B 2 O 3   
                 1.81 
                 2.22 
                 2.69 
                 1.42 
                 1.99 
                 2.02 
               
               
                 (Li 2 O + Na 2 O + K 2 O) 
                 1.25 
                 1.17 
                 1.09 
                 1.26 
                 1.16 
                 1.18 
               
               
                 Li 2 O/(Li 2 O + Na 2 O + K 2 O) 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
                 0.98 
               
               
                 T L  (° C.) 
                 1231 
                 1219 
                 1236 
                 1266 
                 1235 
                 1220 
               
               
                 T F  (° C.) 
                 1349 
                 1362 
                 1368 
                 1317 
                 1379 
                 1303 
               
               
                 T F  − T L  (° C.) 
                 118 
                 143 
                 132 
                 51 
                 144 
                 83 
               
               
                 D k  @ 1 GHz 
                 5.4 
                 5.38 
                 5.39 
                 5.54 
                 5.52 
                 5.58 
               
               
                 D f  @ 1 GHz 
                 0.0016 
                 0.0013 
                 0.002 
                 0.0015 
                 0.0016 
                 0.0015 
               
               
                 Fiber density (g/cm 3 ) 
                 2.393 
                 2.398 
                 2.407 
                 *** 
                 *** 
                 *** 
               
               
                 Fiber strength (MPa) 
                 3954 
                 3977 
                 4076 
                 *** 
                 *** 
                 *** 
               
               
                 Young&#39;s Modulus (GPa) 
                 73.84 
                 80.34 
                 81.57 
                 80.69 
                 81.80 
                 *** 
               
               
                 Fiber failure strain (%) 
                 5.36 
                 4.95 
                 5.00 
                 4.68 
                 4.72 
                 *** 
               
               
                   
               
             
          
         
       
     
         [0179]    It is to be understood that the present description illustrates aspects of the invention relevant to a clear understanding of the invention. Certain aspects of the invention that would be apparent to those of ordinary skill in the art and that, therefore, would not facilitate a better understanding of the invention have not been presented in order to simplify the present description. Although the present invention has been described in connection with certain embodiments, the present invention is not limited to the particular embodiments disclosed, but is intended to cover modifications that are within the spirit and scope of the invention.