Glasses combining high chemical resistance, advantageous thermal expansion properties and good melting properties

Abstract

The invention relates to glasses and glass products which combine good alkali, acid and hydrolytic resistance with advantageous thermal expansion properties. Also, according to the invention are manufacturing processes for such glasses and their uses.

Description

[0001] Glasses combining high chemical resistance, advantageous thermalexpansion properties and good melting properties The invention relates to glasses and glass products which combine good alkali, acid and hydro- lytic resistance with advantageous thermal expansion properties. Manufacturing processes for such glasses and their applications are also part of the invention. State of the art Glasses with good alkali, acid and hydrolytic resistance are required for many applications, es- pecially for pharmaceutical packaging. In general, a certain coefficient of thermal expansion isalso required. Furthermore, these glasses should have good melting properties, i.e. the workingpoint should be below a maximum value.Boron-free variants are also desired. There is a wealth of regulations and standards for characterizing hydrolytic and alkali re-sistance, in particular DIN 12116:2001-03 for acid resistance (herein referred to as DIN 12116),ISO 719:2020-09 for hydrolytic resistance (herein referred to as ISO 719) and ISO 695:1991-05for alkali resistance (herein referred to as ISO 695).Object In the state of the art, there is a lack of glasses that combine good hydrolytic resistance accord- ing to ISO 719 with low removal rates in the alkali resistance test according to ISO 695 and in the acid resistance test according to DIN 12116, and at the same time fulfill the requirement foradvantageous thermal expansion properties and a working point that is well suited for produc-tion. In addition, it should be possible to manufacture the glasses using modern tube drawing production methods.The object is solved by the subject-matter of the patent claims.Description of the inventionBoth the hydrolytic resistance according to ISO 719 and the alkali resistance according to ISO695 essentially reflect the resistance of the glass to an attack by hydroxyl ions. In the case ofISO 695, the concentration of hydroxyl ions in the alkali is set by using a buffer solution contain-ing 0.5 mol / l sodium hydroxide and 0.25 mol / l sodium carbonate. In the case of ISO 719, the15 December 2023 1 / 59 glass is placed in neutral water, the pH of which is initially adjusted to 5.5 (checked by methyl red indicator solution), but very quickly moves into the alkaline range as the glass dissolves. A buffer solution is formed from the weak acids (or acid anhydrides) contained in the glass, namely silicic acid and boric acid, and strong alkalis (such as sodium hydroxide), whose pH is in the range 9 to 10, see Susanne Fagerlund, Paul Ek, Mikko Hupa and Leena Hupa: On deter- mining chemical durability of glasses, Glass Technol.: Eur. J. Glass Sci. Technol. A, December2010, 51 (6), 235-240. The pKa values of the weak acid(s) are decisive for the pH of a buffersolution, with the pKa value of boric acid being approx.0.5 below the pKa value of ortho-silicicacid; the latter is the type of silicic acid that occurs in dilute solutions, see Roland Benedix, Bauchemie für das Bachelorstudium, Springer Vieweg, Wiesbaden, 2014, p.129. The concen-tration of hydroxyl ions is set by the pH of the resulting buffer solution, which depends on theglass type and increases with the dissolution progress. The dissolution caused by these hy-droxyl ions then follows the same mechanism as for the alkali resistance measurement. Thus, to make a glass resistant to both alkali and hydrolytic attack, firstly the removal rate must be set to a low value in the ISO 695 test. Secondly, the pH value must be limited, which resultsduring a test according to ISO 719 and the dissolution of a certain amount of glass in the aque-ous test solution that takes place during this test. The higher this pH value increases during the test, the greater the risk of a positive feedback effect: as the pH increases, the removal rate in- creases, and as the amount of removal in the aqueous solution increases, its pH value in turn increases, and so on. Chemically resistant glasses (hydrolytic class HGB I according to ISO 719) typically experiencea removal during the test that results in 100 µmol of glass in the aqueous solution or less, andthe lower the removal, the less congruent it generally is. Since a comparison of glasses must be based on fixed ratios, we now define the governing pH to be that pH which results after 50 µmol of glass is assumed to dissolve congruently in one literof neutral water. According to the invention, glasses are preferred in which this pH is less than9.50, less than 9.40, less than 9.30, less than 9.20, less than 9.10, less than 9,00, less than8.95, less than 8.90, less than 8.85 or less than 8.80, for example less than 8.75, less than8.70, or less than 8.65. This refers to the pH value resulting from the solution of the system ofequations (1). In some embodiments, the pH is at least 7.95, at least 8.00, at least 8.05, at least8.10, at least 8.15, at least 8.20, at least 8.25, at least 8.30, at least 8.35, at least 8.40, at least8.45, at least 8.50, or at least 8.55. In some embodiments, the pH is in a range of from 7.95 to<9.50, for example from 8.00 to <9.40, from 8.05 to <9.30, from 8.10 to <9.20, from 8.15 to<9.10, from 8.20 to <9.00, from 8.25 to <8.95, from 8.30 to <8.90, from 8.35 to <8.85, from 8.40to <8.80, from 8.45 to <8.75, from 8.50 to <8.70, or from 8.55 to <8.65.15 December 2023 2 / 59 According to the invention, the removal rate corresponding to ISO 695 is preferably at most 85 mg / (dm23h), more preferably at most 80 mg / (dm23h), more preferably at most 75 mg / (dm23h), more preferably at most 70 mg / (dm23h), particularly preferably at most 65 mg / (dm23h), most particularly at most 60 mg / (dm23h), most preferably at most 55 mg / (dm23h). In some embodi- ments, the removal rate corresponding to ISO 695 is at least 5 mg / (dm23h), for example at least 10 mg / (dm23h), at least 15 mg / (dm23h), at least 20 mg / (dm23h), at least 25 mg / (dm23h), at least 30 mg / (dm23h), or at least 35 mg / (dm23h). In some embodiments, the removal rate correspond- ing to ISO 695 is in a range of from 5 to 85 mg / (dm23h), for example from 10 to 80 mg / (dm23h), from 15 to 75 mg / (dm23h), from 20 to 70 mg / (dm23h), from 25 to 65 mg / (dm23h), from 30 to 60 mg / (dm23h), or from 35 to 55 mg / (dm23h). This refers to the removal rate, which can be calcu- lated using formula (2) for glasses of the present invention. Acid resistance describes the resistance of the glass to dissolution of cations at the surface and their replacement by network-destroying hydronium ions. According to the invention, the result- ing removal rate is preferably at most 0.80 mg / (dm26h), more preferably at most 0.75mg / (dm26h), more preferably at most 0.70 mg / (dm26h), more preferably at most 0.65mg / (dm26h), particularly preferably at most 0.60 mg / (dm26h), very particularly preferably at most0.55 mg / (dm26h), most preferably at most 0.50 mg / (dm26h). What is meant is the removal rate,which can be calculated using formula (19) for glasses of the present invention. In some em-bodiments, the removal rate is at least 0.05 mg / (dm26h), for example at least 0.10 mg / (dm26h), at least 0.15 mg / (dm26h), at least 0.20 mg / (dm26h), at least 0.25 mg / (dm26h), at least 0.30 mg / (dm26h), or at least 0.35 mg / (dm26h). In some embodiments, the removal rate is in a range of from 0.05 to 0.80 mg / (dm26h), for example from 0.10 to 0.75 mg / (dm26h), from 0.15 to 0.70 mg / (dm26h), from 0.20 to 0.65 mg / (dm26h), from 0.25 to 0.60 mg / (dm26h), from 0.30 to 0.55 mg / (dm26h), or from 0.35 to 0.50 mg / (dm26h).According to the invention, the coefficient of thermal expansion (CTE) is preferably in a range offrom 2.50 to 6.50 ppm / K, more preferably from 2.75 to 6.25 ppm / K, such as for example from3.00 to 6.00 ppm / K, from 3.25 to 5.75 ppm / K, or from 3.50 to 5.50 ppm / K. In some embodi-ments, the CTE is at least 2.50 ppm / K, at least 2.75 ppm / K, at least 3.00 ppm / K, at least 3.25ppm / K, or at least 3.50 ppm / K. In some embodiments, the CTE is at most 6.50 ppm / K, at most6.25 ppm / K, at most 6.00 ppm / K, at most 5.75 ppm / K, or at most 5.50 ppm / K. This refers to thevalue CTE, which can be calculated using formula (21) for glasses of this invention.According to the invention, the working point is preferably at most 1400°C, more preferably atmost 1375°C, more preferably at most 1350°C, more preferably at most 1340°C, more prefera-bly at most 1325°C, more preferably at most 1300°C, more preferably at most 1290°C, morepreferably at most 1280°C, most preferably at most 1270°C, still more preferably at most15 December 2023 3 / 591260°C, most preferably at most 1250°C. This refers to the working point WP, which can be cal-culated using formula (29) for glasses of the invention. In some embodiments, the working pointWP is at least 950°C, for example at least 975°C, at least 1000°C, at least 1025°C, at least 1050°C, at least 1075°C, at least 1100°C, at least 1125°C, at least 1150°C, at least 1175°C, or at least 1200°C. In some embodiments, the working point WP is in a range of from 950°C to 1400°C, for example from 975°C to 1375°C, from 1000°C to 1350°C, from 1025°C to 1340°C, from 1050°C to 1325°C, from 1075°C to 1300°C, from 1100°C to 1290°C, from 1125°C to 1280°C, from 1150°C to 1270°C, from 1175°C to 1260°C, or from 1200°C to 1250°C.The annealing point AP is preferably in a range of from 575°C to 900°C, for example from600°C to 875°C, from 625°C to 850°C, from 650°C to 825°C, from 675°C to 800°C, or from 700°C to 775°C. This refers to the annealing point AP, which can be calculated using formula (30) for glasses of the invention. In some embodiments, the annealing point AP is at least 575°C, for example at least 600°C, at least 625°C, at least 650°C, at least 675°C, or at least 700°C. In some embodiments, the annealing point AP is at most 900°C, for example at most 875°C, at most 850°C, at most 825°C, at most 800°C, or at most 775°C. Where the present disclosure refers to certain glass properties such as removal rates corre- sponding to ISO 695 or DIN 12116, CTE, working point WP, annealing point AP or other proper- ties that can be calculated by the formulas of the invention, the disclosure refers to the respec- tive calculated values unless indicated otherwise. Thus, if the disclosure for example indicates that the glasses of the invention have a CTE in a certain range or that a removal rate or working point or so on have certain values, this refers to the values calculated using the formulas dis- closed herein unless indicated otherwise.The object is solved by a specific combination of stoichiometric glasses, i.e. glasses which existin the same stoichiometry also as crystals and whose properties can be assumed to be verysimilar for both glass and crystal because of the identical topology of the assemblies - as veri-fied in the literature in many examples by NMR measurements or the like. For this purpose, such stoichiometric glasses are selected whose mixture makes a behavior in the sense of a so-lution of the object according to the invention attainable. In this application, these stoichiometricglasses are also referred to as "constituent phases". It is not a new concept to describe glasses on the basis of the constituent phases to be as- signed to them. By specifying the constituent phases, conclusions can be drawn about the chemical structure of a glass (see Conradt R: "Chemical structure, medium range order, and crystalline reference state of multicomponent oxide liquids and glasses", in Journal of Non-Crys- talline Solids, Volumes 345-346, 15 October 2004, Pages 16-23).15 December 2023 4 / 59In one aspect, the invention relates to a glass having the following combination of constituentphases: Table 1 Constituent PhaseMin (Mol%) Min (Mol%) Max (Mol%)Reedmergnerite (Na2O∙B2O3∙6SiO2) / 8 0 50Potassium-Reedmergne-(K2O∙B2O3∙6SiO2) / 8 0 25rite Albite (Na2O∙Al2O3∙6SiO2) / 8 0 15Sodium-Zinc-Silicate (Na2O∙ZnO∙3SiO2) / 5 0 35Cordierite (2MgO∙2Al2O3∙5SiO2) / 9 0 15Vlasovite (Na2O∙ZrO2∙4SiO2) / 6 0 30Calcium-Zirkonium-Sili-(2CaO∙ZrO2∙4SiO2) / 7 0 30cate Potassium-Niobium-Sili-(K2O∙Nb2O5∙4SiO2) / 6 0 50cate Silicon Dioxide SiO2 15 60Diboron Trioxide B2O3 0 10The composition is chosen with regard to the phases constituting the glass within the limits de- scribed herein. The phases constituting the glass are, of course, not present as such in theglass product in crystalline, but amorphous form. This does not mean, however, that the constit-uent phases have completely different assemblies in the amorphous state than in the crystalline state. As stated above, the topology of the assemblies is comparable, e.g., the coordination of the cations involved with surrounding oxygen atoms or the interatomic distance resulting from the coordination and the strength of the bond between these cations and surrounding oxygen atoms. Therefore, many properties of the glass of the invention can be well described on the ba- sis of the constituent phases, in particular to illustrate the inventive achievement and the prob- lems overcome by the invention. Of course, the glass can be produced not only by using the corresponding crystals, but also by using the usual glass raw materials, as long as only the stoi- chiometric ratios allow the formation of the corresponding building blocks of the basic glasses. In one aspect, the invention relates to a glass comprising the following components in the indi- cated amounts (in mol%): Component Min MaxSiO2 70 85ZrO2 0 5Nb2O5 0 8B2O3 0 9Al2O3 0 3ZnO 0 715 December 2023 5 / 59MgO 0 3CaO 0 8Na2O 0 8K2O 0 8wherein the sum of the amounts of ZrO2and Nb2O5is at least 1.0 mol%, wherein the sum of the amounts of Na2O and K2O is at least 3.0 mol%, wherein the composition of the glass is charac- terized by the following constituent phases (in mol%): Constituent Phase Min MaxReedmergnerite 0 50Potassium-Reedmergnerite 0 25Albite 0 15Sodium-Zinc-Silicate 0 35Cordierite 0 15Vlasovite 0 30Calcium-Zirconium-Silicate 0 30Potassium-Niobium-Silicate 0 50Silicon Dioxide 15 60Diboron Trioxide 0 10wherein the sum of the amounts of Vlasovite, Calcium-Zirconium-Silicate and Potassium-Nio- bium-Silicate is at least 5.0 mol%. In one aspect, the invention relates to a glass comprising the following components in the indi- cated amounts (in mol%): Component Min MaxSiO2 75 85ZrO2 1 3Nb2O5 0 7B2O3 0 8Al2O3 0 2ZnO 0 6MgO 0 2CaO 1 6Na2O 0.5 6K2O 0 7wherein the sum of the amounts of ZrO2and Nb2O5is at least 1.0 mol%, wherein the sum of the amounts of Na2O and K2O is at least 4.0 mol%, wherein the composition of the glass is charac- terized by the following constituent phases (in mol%): Constituent Phase Min MaxReedmergnerite 0 40Potassium-Reedmergnerite 0 20Albite 0 515 December 2023 6 / 59Sodium-Zinc-Silicate 0 30Cordierite 0 10Vlasovite 0 15Calcium-Zirconium-Silicate 1 25Potassium-Niobium-Silicate 0 45Silicon Dioxide 20 55Diboron Trioxide 0 5wherein the sum of the amounts of Vlasovite, Calcium-Zirconium-Silicate and Potassium-Nio- bium-Silicate is at least 5.0 mol%. The phases are selected with regard to their influence on alkali, acid and hydrolytic resistance as well as thermal expansion and working point. In the following, calculation methods are given for calculating these five variables from a given composition of constituent phases. These calcu- lation methods are decisive both for the selection of the constituent phases and for the composi- tion of a glass according to the invention from these constituent phases. Calculation of the pH value in the aqueous solution in the hydrolytic resistance test The calculation of the pH in aqueous solution is based on the composition in simple oxides. In the dilute solution of the glass components, the corresponding cations pass into the most highlyoxidized hydroxides, see Table 4. The release of an H+ or OH- of these hydroxides is describedin each case by a corresponding pKa or pKb value.We refer to the pH value after dissolution of 50 µmol in one liter of the aqueous solution after cooling to room temperature (25°C). The glass fraction of Nb2O5is not considered because of the extremely low solubility of Nb(OH)5, see M. Filella, Peter M. May, The aqueous solution thermodynamics of niobium under conditions of environmental and biological interest, Applied Geochemistry 122 (2020) 104729.Table 2# Oxide or Acid orAnhydride Hydroxide 1. SiO2 H4SiO4 H4SiO4→ H3SiO4- + H+ pKa = 9.71)H3SiO4- → H2SiO4-2 + H+ pKa = 11.91)2. ZrO2 Zr(OH)4 Zr(OH)4 + H2O → Zr(OH)5- + H+ pKa = 5.992)Zr(OH)3+ + H2O → Zr(OH)4 + H+ pKa = 4.62)15 December 2023 7 / 59# Oxide or Acid orAnhydride Hydroxide 3. Al2O3 Al(OH)3 Al(OH)3 + H2O → Al(OH)4- + H+ pKa = 12.33)Al(OH)2++H2O→ Al(OH)3 + H+ pKa = 5.73)4. ZnO Zn(OH)2 Zn+2+H2O→ ZnOH+ + H+ pKa = 9.054)ZnOH++H2O→ Zn(OH)2 + H+ pKa = 9.754)Zn(OH)2 +H2O→ Zn(OH)3- + H+ pKa = 10.14)Zn(OH)3- +H2O→ Zn(OH)4- + H+ pKa = 10.054)5. MgO Mg(OH)2 Mg(OH)2→ Mg(OH)+ + OH- pKb = -25)Mg(OH)+→ Mg+++ OH- pKb = 2.586) 6. CaO Ca(OH)2 Ca(OH)2→ Ca(OH)+ + OH- pKb = -25)Ca(OH)+→ Ca+++ OH- pKb = 1.37) 7. Na2O NaOH NaOH → Na+ + OH- pKb = -0.7710)8. K2O KOH KOH → K+ + OH- pKb = -211)10. SrO Sr(OH)2 Sr(OH)2→ Sr(OH)+ + OH- pKb = -25)Sr(OH)+→ Sr+++ OH- pKb = 0.8212) 11. BaO Ba(OH)2 Ba(OH)2→ Ba(OH)+ + OH- pKb = -25)Ba(OH)+→ Ba+++ OH- pKb = 0.6413)1) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 176; value from the source des- ignated there as "G40".2) R.H. Byrne, Inorganic speciation of dissolved elements in seawater: the influence of pH on concentration ratios, Geochem. Trans.3 (2) (2002) 11-16.3) David W. Hendricks, Water Treatment Unit Processes: Physical and Chemical, CRC Taylor and Francis, Boca Raton, London, New York, 2006, p.307; values from sources labeled "4", "5", "11", "12" there.4) Artur Krezel, Wolfgang Maret, The biological inorganic chemistry of zinc ions, Archives of Bio- chemistry and Biophysics (2016), pp.1-17.15 December 2023 8 / 595) As for barium hydroxide, see Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 12, we assume that the M(OH)2→ M(OH)++ OH- for all alkaline earths M proceeds fully in each case; we set as the pKb value for this first dissociation the highest pKb value occurring in this table, namely that of potassium hydroxide.6) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 115; value from the source des- ignated there as "S74".7) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 18; value from source desig- nated there as "D9".10) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 178; value from source desig- nated there as "G26".11) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 164; value from source desig- nated there as "K2".12) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 180; value from source desig- nated there as "G26".13) Pure Appl. Chem., 1969, Vol.20, No.2, pp.133-236, number 12; value from source desig- nated there as "D7". The pH value follows for a given composition by solving the system of equations for the variousconcentrations [...] (for pKa and pKb the values listed above are to be inserted):System of equations (1)1. [H2SiO4- -] [H+] / [H3SiO4-] = 10-pKa,2. [H3SiO4-] [H+] / [H4SiO4] = 10-pKa,3. [H2SiO4- -] + [H3SiO4-] + [H4SiO4] = 50 (µmol / l) * cSiO2,4. [Zr(OH)5-] [H+] / [Zr(OH)4] = 10-pKa,5. [Zr(OH)4] [H+] / [Zr(OH)3+] = 10-pKa,6. [Zr(OH)5-] + [Zr(OH)4]+ [Zr(OH)3+] = 50 (µmol / l) * cZrO2,7. [Al(OH)4-] [H+] / [Al(OH)3] = 10-pKa8. [Al(OH)3] [H+] / [Al(OH)2+] = 10-pKa,9. [Al(OH)4-] + [Al(OH)3] + [Al(OH)2+] = 50 (µmol / l) * 2 * cAl2O3,10. [ZnOH+] [H+] / [Zn++] = 10-pKa,15 December 2023 9 / 5911. [Zn(OH)2] [H+] / [ZnOH+] = 10-pKa,12. [Zn(OH)3-] [H+] / [Zn(OH)2] = 10-pKa,13. [Zn(OH)4- -] [H+] / [Zn(OH)3-] = 10-pKa,14. [ZnOH+] + [Zn++] + [Zn(OH)2] + [Zn(OH)3-] + [Zn(OH)4- -] = 50 (µmol / l) * cZnO,15. [MgOH+] [OH-] / [Mg(OH)2] = 10-pkb16. [Mg++] [OH-] / [MgOH+] = 10-pkb,17. [MgOH+] + [Mg(OH)2] + [Mg++] = 50 (µmol / l) * cMgO,18. [CaOH+] [OH-] / [Ca(OH)2] = 10-pkb19. [Ca++] [OH-] / [CaOH+] = 10-pkb,20. [CaOH+] + [Ca(OH)2] + [Ca++] = 50 (µmol / l) * cCaO,21. [SrOH+] [OH-] / [Sr(OH)2] = 10-pkb22. [Sr++] [OH-] / [SrOH+] = 10-pkb,23. [SrOH+] + [Sr(OH)2] + [Sr++] = 50 (µmol / l) * cSrO,24. [BaOH+] [OH-] / [Ba(OH)2] = 10-pkb25. [Ba++] [OH-] / [BaOH+] = 10-pkb,26. [BaOH+] + [Ba(OH)2] + [Ba++] = 50 (µmol / l) * cBaO,27. [Na+] [OH-] / [NaOH] = 10-pkb,28. [Na+] + [NaOH] = 50 (µmol / l) * 2 * cNa2O,29. [K+] [OH-] / [KOH] = 10-pkb,30. [K+] + [KOH] = 50 (µmol / l) * 2 * cK2O,31. [OH-] [H+] = 10-14,32. 2*[H2SiO4- -] + [H3SiO4-]+ [Zr(OH)5-] + [Al(OH)4-] + 2*[Zn(OH)4- -] + [Zn(OH)3-] + [OH-] =[Zr(OH)3+] + [Al(OH)2+] + 2*[Zn++] + [ZnOH+] + 2*[Ba++] + [BaOH+] + 2*[Sr++] + [SrOH+] + 2*[Ca++] + [CaOH+] + 2* [Mg++] + [MgOH+] + [Na+] + [K+] + [H+]Equations 1 - 31 are equilibrium conditions, and equation 32 is the electroneutrality condition.The system of equations is uniquely solvable using one of the commonly available mathemati- cal codes, such as MATHEMATICA from Wolfram Research Inc. MATHEMATICA provides a list of solutions, but only one of them satisfies the necessary additional condition that all concentra- tions must have positive values.15 December 2023 10 / 59 The pH value follows by definition as the negative decadic logarithm of [H+]. Since a comparison of glasses must be based on fixed ratios, we now define the governing pH to be that pH which results after 50 µmol of glass is assumed to dissolve congruently in one literof neutral water. According to the invention, glasses are preferred in which this pH is less than9.50, less than 9.40, less than 9.30, less than 9.20, less than 9.10, less than 9,00, less than8.95, less than 8.90, less than 8.85 or less than 8.80, for example less than 8.75, less than8.70, or less than 8.65. This refers to the pH value resulting from the solution of the system ofequations (1). In some embodiments, the pH is at least 7.95, at least 8.00, at least 8.05, at least8.10, at least 8.15, at least 8.20, at least 8.25, at least 8.30, at least 8.35, at least 8.40, at least 8.45, at least 8.50, or at least 8.55. In some embodiments, the pH is in a range of from 7.95 to <9.50, for example from 8.00 to <9.40, from 8.05 to <9.30, from 8.10 to <9.20, from 8.15 to <9.10, from 8.20 to <9.00, from 8.25 to <8.95, from 8.30 to <8.90, from 8.35 to <8.85, from 8.40 to <8.80, from 8.45 to <8.75, from 8.50 to <8.70, or from 8.55 to <8.65. Calculation of alkali resistance according to ISO 695 At this point, the invention is based on a surprisingly found correlation between a quantity con- structed with the help of topological considerations and the removal rate measured in the test according to ISO 695. The essence of topological considerations is, as explained in detail in DE 102014119594 A1, to count the constraints imposed on the atoms by the bond to the neighboring atoms. Theseconstraints concern on the one hand the interatomic distance ("distance constraints"), on theother hand the bond angles ("angle constraints"). If an atom has r neighbors (r = coordinationnumber), then from the r distance conditions to these neighbors it follows that r / 2 distance con-ditions have to be assigned to this atom, if one distributes the distance conditions equally among both bonding partners. From the bond angles between these neighbors, with the atomunder consideration at the apex of the respective angle, it follows that further 2r-3 angle condi-tions have to be assigned to this atom. In DE 102014119594 A1 a method is described which, when calculating the distance and an- gle conditions, provides for a weighting of all conditions with the single bond strength and again an additional weighting of the angle conditions (only those originating from the oxygen-cation- oxygen angles; the conditions belonging to the cation-oxygen-cation angles are neglected) with the degree of covalency of the respective bond. The weighting factors are normalized by divid- ing each by the single bond strength or the degree of covalency of the silicon-oxygen bond, so that for fused silica a number of (rounded) 1.3333333 (i.e.4 / 3) distance conditions and15 December 2023 11 / 59 (rounded) 1.666666667 (i.e.5 / 3) angle conditions per atom results. This is consistent with the direct analysis of the topology of fused silica, as stated in DE 102014119594 A1, if one simply counts all spacing and angular conditions and neglects the angular conditions of the silicon-oxy- gen-silicon angles. Thus, fused quartz has a number of "3" constraint conditions per atom, which is exactly equal to the number of degrees of freedom per atom. Quartz glass should therefore have no (or realiter: a very small) number of degrees of freedom per atom, which corresponds to the small cp jump of fused quartz in the glass transition measured by differential calorimetry, see R. Brüning, "On the glass transition in vitreous silica by differential thermal analysis measurements," Journal of Non-Crystalline Solids 330 (2003) 13-22. For other oxide glasses, generally lower values for the numbers of distance and angle terms per atom than (rounded) 1.3333333 (4 / 3) and 1.666666667 (5 / 3), respectively, are obtained. The differences between 1.3333333 (4 / 3) and 1.666666667 (5 / 3), respectively, and those lower val- ues are correspondingly equal to the numbers of the distance and angular degrees of freedom per atom, respectively. In the case of the angular degrees of freedom, one can still distinguish whether the associated angular conditions refer to angles which all lie in one plane (trigonal co- ordination) or not (tetrahedral or higher coordination). The latter are here called 3D angle condi- tions; the difference between 1.6666667 (5 / 3) and the number of 3D angle conditions is corre-spondingly called the number of 3D angular degrees of freedom.Surprisingly, a correlation is found between the number of 3D angular degrees of freedom per atom and the removal rate r in the ISO 695 test, which can be used to estimate the position of a glass with respect to the alkali resistance classes. This relationship can be understood in the sense that the more possible positions are available in the network, the more likely it is that a hydroxyl ion will penetrate, and the more structural degrees of freedom there are in the system,the greater the number of these positions. For f = 0 the number of possible positions in fusedsilica is given. A mathematical expression for the relationship between the number of 3D angular degrees offreedom per atom and the removal rate r in the ISO 695 test, which is also suitable for theglasses according to the present invention and has been tested on a large number of glasses, is: 15 December 2023 12 / 59 According to the invention, the removal rate corresponding to ISO 695 is preferably at most 85 mg / (dm23h), more preferably at most 80 mg / (dm23h), more preferably at most 75 mg / (dm23h), more preferably at most 70 mg / (dm23h), particularly preferably at most 65 mg / (dm23h), most particularly at most 60 mg / (dm23h), most preferably at most 55 mg / (dm23h). In some embodi- ments, the removal rate corresponding to ISO 695 is at least 5 mg / (dm23h), for example at least 10 mg / (dm23h), at least 15 mg / (dm23h), at least 20 mg / (dm23h), at least 25 mg / (dm23h), at least 30 mg / (dm23h), or at least 35 mg / (dm23h). In some embodiments, the removal rate correspond- ing to ISO 695 is in a range of from 5 to 85 mg / (dm23h), for example from 10 to 80 mg / (dm23h), from 15 to 75 mg / (dm23h), from 20 to 70 mg / (dm23h), from 25 to 65 mg / (dm23h), from 30 to 60 mg / (dm23h), or from 35 to 55 mg / (dm23h). This refers to the removal rate, which can be calcu- lated using formula (2) for glasses of the present invention. "f" is the number of 3D angular degrees of freedom per atom. The exponent "4" is a value found empirically to be suitable; in addition, the number "6" is also commonly used. The constants "c"and " c' " are chosen in such a way that in interaction with the value "4" for the exponent an opti-mal reproduction of the removal rate results in the ISO 695 test. "c" is a constant with dimensionmg / (dm23h); the numerical value is 356.23. " c' " is a dimensionless constant with value 0. Λ isthe optical basicity. The factor N / NSiO2is used to convert from an atomic group, on which the above probability con- sideration has been made, to a mole. N is the number of atoms per mole. NSiO2is the number of atoms per mole of fused silica (namely 3NA, NAAvogadro number) and is used to normalize this expression. One can set this factor equal to a constant without much error and drag this con- stant into the prefactor "c" if one is only within a narrowly defined glass family. The factor M / MSiO2 is used to convert the above atomic consideration to a mass consideration. M is the mass of a mole. MSiO2is the mass of one mole of quartz glass (namely 60.084g) and serves to normalize this expression. It is also possible to set this factor equal to a constant without large error and to include this constant in the prefactor "c", if one is only within a narrowly circum- scribed glass family.The correlation between the removal rate and the number of 3D angular degrees of freedomhas been found empirically, as mentioned above, but seems plausible in view of the fact that the kinetics of the penetration of OH- ions into the glass depends on the entropy of the glass. The factor (0.9483333-Λ) is not associated with the kinetics of the process, but with the driving force of the acid-base reaction occurring in the course of dissolution of the glass in the alkali.15 December 2023 13 / 59 Since the glasses according to the invention have a combination of the constituent phases indi- cated above, it is convenient for the calculation of the number of 3D angular degrees of freedom per atom to first specify them numerically for each constituent phase. It holds: Table 3 Constituent PhaseFormula (normalized to Atoms perNumber of 3D a simple oxide) building unit angular degrees of freedom per atom Reedmergnerite (Na2O∙B2O3∙6SiO2) / 8 26 / 8 0.235470229Potassium-Reedmerg-(K2O∙B2O3∙6SiO2) / 8 26 / 8 0.238787725nerite Albite (Na2O∙Al2O3∙6SiO2) / 8 26 / 8 0.318898019Sodium-Zinc-Silicate (Na2O∙ZnO∙3SiO2) / 5 17 / 6 0.52778666Cordierite (2MgO∙2Al2O3∙5SiO2) / 9 29 / 9 0.427525473Vlasovite (Na2O∙ZrO2∙4SiO2) / 6 3 -0.35Calcium-Zirkonium-Sili-(2CaO∙ZrO2∙4SiO2) / 7 19 / 7 -0.1cate Potassium-Niobium-Si-(K2O∙Nb2O5∙4SiO2) / 6 22 / 6 0.1licate Silicon Dioxide SiO2 3 0Diboron Trioxide B2O3 5 1.666666667The numerical values for the zirconium- and niobium-free compounds have been calculated ac-cording to the procedure given in DE 102014119594 A1, where here the number of angular degrees of freedom has been calculated for all cations and in the same way as in DE 102014 119594 A1 (but there only for boron and aluminum); furthermore, the degree of ionization of a cation-oxygen compound has not been calculated according to formula (8) from DE 102014 119594 A1, but according to formula (3) from Alberto Garcia, Marvon Cohen, First Principles Ionicity Scales, Phys. Rev. B 1993. In addition, one needs information about the coordination number of the respective cation, for which, according to Conradt, loc.cit., the coordination num- ber in the respective constituent phase is used (if a cation occurs in several coordination num- bers, the average is taken according to the proportions in the different coordination numbers). The mentioned coordination numbers are taken from the literature, for reedmergnerite: D.E. Ap- pleman, J.R. Clark, Crystal structure of reedmergnerite, a boron albite, and its relation to feld- spar crystal chemistry, American Mineralogist 50 (1965) 1827-1850, with respect to which source silicon and boron are assumed to be 4-fold and sodium 5-fold coordinated; for potassium reedmergnerite: M. Kimata, Crystal structure of KBSi3O8 isostructural with danburite, Miner- alogical Magazine 57 (1993) 157-164, with respect to which source silicon and boron are as-sumed to be 4-fold and potassium 8-fold coordinated; for albite: R. T. Downs, A. Andalman, M.Hudacsko, The coordination numbers of Na and K atoms in low albite and microcline as15 December 2023 14 / 59 determined from a procrystal electron-density distribution, American Mineralogist 81 (1996) 1344-1349, with respect to which source silicon and aluminum are assumed to be 4-fold and so- dium 5-fold coordinated; for cordierite: P. Daniels, Structural effects of the incorporation of large radius alkalis in high cordierite, American Mineralogist 77 (1992) 407-411, with respect to which source silicon and aluminum are assumed to be 4-fold and magnesium 6-fold coordinated; for vlasovite: E. Sokolova, F. C. Hawthorne, N. A. Ball, R. H. Mitchell, G. Della Ventura, Vlasovite, Na2 Zr (Si4O11), from the Kipawa Alkaline Complex, Quebec, Canada: crystal-structure refine- ment and infrared spectroscopy, The Canadian Mineralogist 44 (2006) 1349-1356, with respect to which source silicon is assumed to be 4-fold coordinated, zirconium 6-fold coordinated, and sodium half 7-fold and half 6-fold coordinated; for Ca2ZrSi4O12: S. Colin, B. Dupre, G. Venturini, B. Malaman, C. Gleitzer, Crystal Structure and Infrared Spectrum of the Cyclosilicate Ca2ZrSi4O12, Journal of Solid State Chemistry 102 no.1 (1993) 242-249, with respect to which source silicon is assumed to be 4-coordinated, zirconium 6-coordinated and calcium half 8-coor- dinated and half 9-coordinated; for KNbSi2O7: A. Sahashi, T. Hoshina, H. Takeda, T. Tsurumi, Fabrication of ferroelectric silicate KNbSi2O7single crystal, Journal of the Ceramic Society of Ja- pan 122 No.6 (2014) 389-392, with respect to which source silicon is assumed to be 4-fold co- ordinated, niobium 6-fold coordinated, and potassium 12-fold coordinated; for Na2ZnSi3O8: K.-. F. Hesse, F. Liebau, H. Böhm, Disodium-Zincosilicate, Na2ZnSi3O8, Acta Crystallica B33 (1977) 1333-1337, with respect to which source silicon is assumed to be 4-fold coordinated, zinc 4-fold coordinated, and sodium half 7-fold coordinated and half 8-fold coordinated; for SiO2, the 4-fold coordination of silicon is assumed to be generally known, see G. Ferlat, A.P. Seitsonen, M. Lazzeri, F. Mauri, Hidden polymorphs drive the vitrification in B2O3, Nature Materials 11 (2012), 925-929.The numerical values for the zirconium- and niobium-containing compounds take into accountthe fact that these compounds offer even fewer possible positions for a penetrating hydroxyl ion than quartz glass because of the spatially tight octahedral coordination of the zirconium or nio- bium ions and the surrounding oxygen ions, which is held together by a large bond strength, see below under "Thermal expansion" under "Potential well depth". The calculation rule for determining the 3D angular degrees of freedom f per atom on the fin- ished glass is thus: (3)where ci is the molar fraction of the i-th constituent phase in the glass composition under consid-eration, zi is the number of atoms per building unit in the i-th constituent phase (or number of15 December 2023 15 / 59atoms per mole in the i-th constituent phase; then in units of NA, NA Avogadro number), and fi isthe number of angular degrees of freedom per atom in the i-th constituent phase. "n" is the num-ber of constituent phases.Notably, throughout the present disclosure the term “ci” refers to the molar fraction of the i-thconstituent phase in the glass composition under consideration, and the term “n” refers to the number of constituent phases, unless indicated otherwise. The calculation rule for the determination of M / MSiO2 is: where ci is the molar fraction of the i-th constituent phase in the glass composition under consid-eration and Mi is the corresponding molar mass. The values of Mi are listed below in Table (5). "n" is the number of constituent phases. The calculation rule for the determination of N / NSiO2 is: where ci is the molar fraction of the i-th constituent phase in the glass composition under consid-eration, and zi is the number of atoms per building unit in the i-th constituent phase (or numberof atoms per mole in the i-th constituent phase; then in units of NA, NA Avogadro number), "n" is the number of constituent phases. The factor (0.9483333-Λ) is related to the driving force of dissolution by the following considera- tion. This driving force is higher the more "acidic" the glass is, i.e., the higher the proportion ofacid anhydrides and the lower the proportion of base anhydrides. A quantitative measure of thisis optical basicity, see C.P. Rodriguez, J.S. McCloy, M.J. Schweiger, J.V. Crum, A, Winschell, Optical Basicity and Nepheline Crystallization in High Alumina Glasses, Pacific Northwest Na- tional Laboratories, PNNL 20184, EMSP-RPT 003, prepared for the US Department of Energy under contract DE-AC05-76RL01830. The lower the optical basicity, the higher the driving force. The case of "driving force equal to zero" exists if the material is one in which the acid-base reac- tion has completely run its course. We assume the latter case in particular if the glass has the stoichiometry of sodium metasilicate, i.e. among all the sodium silicates occurring as solids, the one with the highest sodium content. (Sodium orthosilicate occurs only in aqueous solution.) Its optical basicity, according to the method of calculating it described below, is just 0.9483333, i.e. the value at which per constructionem the above factor (0.9483333-Λ) becomes zero.15 December 2023 16 / 59We calculate the optical basicity Λ according to formula B.1 with the coefficients Λχav (optical ba-sicity according to Li and Xue) according to section B.1.6 and table B.1 From C.P. Rodriguez, J.S. McCloy, M.J. Schweiger, J.V. Crum, A, Winschell, Optical Basicity and Nepheline Crystalli- zation in High Alumina Glasses, Pacific Northwest National Laboratories, PNNL 20184, EMSP- RPT 003, prepared for the US Department of Energy under contract DE-AC05-76RL01830. For- mula B.1 first contains a sum over all simple oxides, where the individual summand is the prod-uct of the number of oxygen atoms to be assigned to that simple oxide and the correspondingcoefficient Λχav, which in turn depends on the cation and the coordination number of the cation. This sum is divided by the total number of oxygen atoms. Said coefficients can be found in Ta- ble B.1, which is arranged according to cations or the corresponding simple oxides. Where only one coefficient is given in the table for the simple oxide thus selected, that coefficient is used. Where several coefficients are given in the table for the selected simple oxide, the one which fits the coordination numbers of the respective cation in the constituent phases is used. If the above formula B.1 is adapted to a glass whose composition is given in constituent phases, we obtain: (6) Where xi,j is the proportion of the j-th simple oxide in the i-th constituent phase, Oe,j is the num- ber of oxygen atoms in the j-th simple oxide, and Λχav,i,j is the number selected according to the j-th cation and its coordination in the i-th constituent phase. Exactly, equation (6) reads: (7) mi is the number of simple oxides in the i-th constituent phase. The αi and βi, i.e. the sums overj, can be tabulated for individual constituent phases to simplify the calculation of optical basicity for the glasses according to the invention: Table 4 Constituent Phase ^i = ∑^^^^^ ^^,^ ∙ ^^,^ ∙ Λ^av,^,^ ^i =∑^^^^^^^,^ ∙ ^^,^Reedmergnerite 1.741875 2Potassium-Reedmergnerite 1.71625 2Albite 1.761375 2Sodium-Zinc-Silicate 1.4472 1.6Cordierite 1.783777778 2Vlasovite 1.621166667 1.833333333Calcium-Zirkonium-Silicate 1.520571429 1.71428571415 December 2023 17 / 59Constituent Phase ^i = ∑^^^^^ ^^,^ ∙ ^^,^ ∙ Λ^av,^,^ ^i =∑^^^^^^^,^ ∙ ^^,^Potassium-Niobium-Silicate 2.002166667 2.333333333Silicon Dioxide 1.696 2Diboron Trioxide 2.355 3For example, a glass composed of 50% silica and 50% diboron trioxide has an optical basicityof (0.5*1.696+0.5*2.355) / (0.5*2+0.5*3) = 4.051 / 5 = 0.8102. Acid resistanceSurprisingly, the removal rate in acid can also be estimated with the aid of a relationship that iseasy to calculate. The starting point for the underlying considerations is first of all the theory of Anderson and Stu- art on ionic mobility in silicate glasses, see O.L. Anderson, D.A. Stuart, Calculation of Activation Energy of Ionic Conductivity in Silica Glasses by Classical Methods, Journal of the AmericanCeramic Society, Vol.37, No. 12 (1954), 573 - 580. According to this, the activation energy ofthe movement of a cation in a silicate and thus oxide glass depends on the one hand on the electrostatic interaction to be overcome with the surrounding oxygen ions and on the other hand on the mechanical resistance to be overcome when changing from one mesh of the silicate net- work to the next. According to Coulomb's law, the first-mentioned contribution is proportional tothe charge number of the cation under consideration and inversely proportional to the dielectricconstant, while the second-mentioned contribution is proportional to the shear modulus and to the square of the amount by which the diameter of the cation under consideration exceeds the mesh size of the network. Because of the first contribution, only singly charged cations are mo- bile and multiply charged cations such as aluminum are stationary. In contact with a highly concentrated acid, which according to ISO 1776 or DIN 12116 is 6N hy- drochloric acid, the situation is different. In this case, protons or hydronium ions diffuse into the glass and form an electrical double layer on the surface with the chloride ions remaining in the acid bath. Analysis of the eluate from measurements carried out according to ISO 1776 has shown that this electric double layer forms to such an extent that the resulting electric field is able to compensate for the electrostatic interaction of the respective cation with the surrounding oxygen ions, so that even ions with a high charge number become mobile. (The force effect of the electric field of the mentioned double layer depends just like the electrostatic interaction of the considered cation on its charge number; the former may therefore be able to compensate the latter). It must be taken into account that the H2O contained in the hydronium ion H3O+addi- tionally weakens the electrostatic interaction because of the very large dielectric permeability of water. Likewise, the swelling of the network weakens the mechanical cohesion.15 December 2023 18 / 59 It is observed that under the same experimental conditions (those of ISO 1776 or DIN 12116), considerably more aluminum ions leave an alkali-free display glass than sodium ions leave a soda-lime glass. This indicates that the decisive property for the mobility of an ion is its radius, which in turn is much smaller for an Al+++ion than for an Na+ion. Thus, it makes more sense to describe the motion of ions in and out of the glass using the theory of the motion of particles in a viscous fluid rather than Anderson and Stuart's theory. According to Stokes-Einstein, the diffu- sion coefficient for a sphere in a viscous fluid is inversely proportional to the viscosity and radius of the sphere. For a simple description of acid attack, we make the following modeling approach. We consider the top atomic layers of the glass: In a first step, a certain number of the cations of these atomic layers diffuse out into the acid. This number is proportional to the respective diffusion coefficient, which in turn is given by: ^^^^^.´ ^^,^=^^,^(8) Here ri,jis the radius of the cation of type "j" in the i-th constituent phase. This gives the loss number Ωi,jof cations of type "j" from the i-th constituent phase: Here zj,i is the number of cations of the j-th type in the i-th constituent phase. The viscosity occurring in the Stokes-Einstein equation has been integrated into the constant “const.´”; we thus assume that the viscosity resulting for the softened, "gel-like" glass is the same for all constituent phases under the experimental conditions. We further assume that the loss of cations occurring in this first step is reflected in the loss balance as a corresponding loss of oxides, i.e. that the result of this first step for one mole of glass is a mass loss ΔM1 of the fol- lowing magnitude: Mej is the molar mass of the simple oxide belonging to the cation of type "j" and aj is the number of cations of type "j" in this oxide. The sum over “i” runs from 1 to n, the sum over “j” runs from 1 to mi, as above. The constant "const." is determined empirically so that the model gives optimal results for the glass composition range according to the invention. The numerical value is:15 December 2023 19 / 59^^^^^. = 0,76Å (11)ΔM1 is thus in the unit g / mol. ri,j is to be used in Å. In a second step, which is mentally separate from the first, the charge balance in the uppermostatomic layers of the glass is balanced again by - this is our model assumption - as many hydro-nium ions penetrating as are necessary for charge compensation. This number Z2 is given for one mole of glass by: wj is the valence of a j-th type cation. The sum over “i” runs from 1 to n, the sum over “j” runsfrom 1 to mi, as above. At the place of each diffused-out cation there are as many H+ ions com-ing from the diffused-in hydronium ions as correspond to the valence of the diffused-out cation. Now, each hydronium ion also contains an H2O, which in turn is capable of dissolving an oxy- gen compound in the glass and replacing it with two hydroxyl groups. If we put Z2 in proportion to the total number of oxygen atoms in the glass, we get an estimate of the fraction of the glass that is dissolved by this dissolving of oxygen compounds. We do not make any difference which cations are on the two sides of the oxygen compounds. The total number of oxygen atoms O in one mole of glass is: O= ∑^ c^ ∙ ^^ (13)Here, Oi is the number of oxygen atoms in the i-th constituent phase. We estimate the resulting mass loss ΔM2 by: ∆^ ^^ = ^ ∙^^ (14) The summed mass loss from steps 1 and 2 is calculated as follows ∆^ = ∆^^ + ∆^^ (15)By exchanging the diffused cations for the equivalent number of H+ions, the top glass layer is further softened and transformed into a gel. The main cation of this gel is silicon, since silicon has the least tendency to diffuse out, as will be shown below.15 December 2023 20 / 59 If it were to remain so in any case, the resulting gel would make diffusion out of and into the glass more difficult, resulting in a lower and lower dissolution rate as dissolution progresses. This is indeed in line with the findings from long-term measurements on acid-resistant glass. However, due to the additional effect of the H2O, parts of this gel are completely dissolved. In the case of acid-resistant glass, this effect is small, so that the finding is as just described, namely that there is a slow dissolution of the glass with a temporally decreasing dissolution rate. What results with less acid-resistant glass can be illustrated in a thought experiment. The start- ing point is an estimate for the size of the fraction of the uppermost glass layer which will disap- pear in steps 1 and 2. One may argue that the size of this fraction may be derived from ^M1 + ^M2. However, as the composition of ^M1 is different from the glass composition, such a deri- vation is not straight-forward.Instead, a simplified starting point is suggested. It is assumed that such a large fraction of theuppermost glass layer will disappear completely as it corresponds to the fraction of the originallypresent oxygen atoms that will be replaced by two OH groups in the course of steps 1 and 2.Each hydronium ion leads to as many OH groups as it contains H atoms, i.e. to three OH groups. Thus, one and a half times as many oxygen atoms are replaced as hydronium ions dif- fuse into the glass.The fraction ε of the uppermost glass layer that completely disappears and thus exposes thenext lower glass layer is therefore given by: We now make the further modeling assumption that the diffusive exchange of an exposed glasslayer in direct contact with the acid occurs rapidly, while the diffusive exchange retarded by agel layer occurs slowly. Thus, we must add to the above mass loss ΔM from equation (15) the mass loss ε∙ΔM that oc-curs at the exposed next lower glass layer. Since this next lower glass layer also completely dis-appears to some fraction sized ε, the whole thing continues in the manner of a geometric series. We obtain ΔMges for the total mass loss: ∆^ ^ ^∆^ ^^^ = ∆^ + ∆^ ∙ ^ + ∆^ ∙ ^ + ∆^ ∙ ^ + ⋯ =^^^ (17)The denominator suggests that catastrophic resolution behavior occurs at ε ≥ 1. This is alsoconfirmed experimentally.15 December 2023 21 / 59 The unit of ΔMges, since "mole" and "molar mass" (in grams) have been used everywhere, is "grams per mole". With the help of a prefactor f, which also includes the time in which ΔMges is removed, it is converted below to "milligrams per decimeter square and six hours" (mg / (dm²6h) to make the quantity comparable with the measured quantity of DIN 12116. The following table is used to calculate the material removal rate for an acid resistance test in accordance with DIN 12116. Table 5 ConstituentStoichiometry ^^^^^.^^^^^.^^Mi∙^^^ Phase^ ^,^^^ ∙^ ∙ ^^^^^,^ ∙ ^^^ ^^,^^^^^^ ^^^^,^Reedmerg-(Na2O∙B2O3∙6SiO2) / 8 9.05021 0.501519 2 61.51275nerite Potassium-(K2O∙B2O3∙6SiO2) / 8 9.30871 0.450004 2 65.53975Reedmerg- nerite Albite (Na2O∙Al2O3∙6SiO2) / 8 23.441 1.24214 2 65.5555Sodium-Zinc-(Na2O∙ZnO∙3SiO2) / 5 24.0227 0.646597 1.6 64.722Silicate Cordierite (2MgO∙2Al2O3∙5SiO2) / 9 40.4059 2.30471 2 64.9944444Vlasovite (Na2O∙ZrO2∙4SiO2) / 6 24.6482 0.798872 2 70.9228333Calcium-Zir-(2CaO∙ZrO2∙4SiO2) / 7 25.0007 0.841821 1.71 67.9588571konium-Sili- cate Potassium-(K2O∙Nb2O5∙4SiO2) / 6 24.4656 0.810568 2.33 100.05656Niobium-Sili- cate Silicon Dio-SiO2 0 0 2 60.084xide Diboron Tri-B2O3 31.0824 2.67882 3 69.619oxideThe quantity ΔM1 is determined by multiplying the numbers in the third column by the ci andthen summing up and subsequently dividing by sum over ci. The quantity Z2 is determined bymultiplying the numbers in the fourth column by the ci and then summing them up and subse-quently dividing by sum over ci. The quantity O is determined by multiplying the numbers in thefifth column by the ci and then summing up and subsequently dividing by sum over ci. The quan-tity M is calculated as above, see (4). Thus, the quantity M is determined by multiplying thenumbers in the sixth column by the ci and then summing up and subsequently dividing by sumover ci. In other words, ΔM1is calculated according to the following formula15 December 2023 22 / 59 wherein the numerical values of μiare those of the third column of Table 5. Z2is calculated according to the following formula wherein the numerical values of ζi are those of the fourth column of Table 5.O is calculated ac- cording to the following formula wherein the numerical values of Oiare those of the fifth column of Table 5. M is calculated according to the following formula wherein the numerical values of Mi are those of the sixth column of Table 5. The following is to be said about the calculation of the quantities listed in the table. The quanti- ties zi,j and Oj result directly from the stoichiometry. The molar masses of the simple oxides are generally known, as are the valences of the cations. For the ionic radii ri,j, the values of R.D. Shannon, Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Hal- ides and Chalcogenides, Acta Cryst. A32 (1976), 751-767, are used. Here we do not refer to the columns marked with "IR", but to those marked with "CR", because of good experiences madein connection with ionic conductivity, see DE102015005836. In every case, the ionic radius ischosen which belongs to the coordination present in the constituent phase. The respective coor- dination number is taken from the above-mentioned literature on the constituent phases. Only the ions of silicon, boron and niobium are handled differently. Silicon exists in acidic aqueous solution as ortho-silicic acid, not as an ion, see S. Sjöberg, Sil- ica in aqueous environments, Journal of Non-Crystalline Solids 196 (1996) 51-57. In view of15 December 2023 23 / 59 both this and the fact that the removal rate for pure silica glass in tests according to DIN 12116 is below the laboratory detection limit, we set the contribution of silicon to the above step 1 equal to zero or assume an infinitely large radius for the silicon ion. Boron exists in acidic aqueous solution as boric acid, although polymerization does not occur in dilute solutions, see Victor Kochkodan, Nawaf Bin Darwish, Nidal Hilal, The chemistry of boron in water, chapter 2 in Boron Separation Processes, Nalan Kabay, Marek Bryjak, Nidal Hilal eds, Elsevier, Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Fran- cisco Sydney Tokyo (2015). We therefore take as radius the radius of a sphere equivalent in volume to B(OH)3. The OH radius is also taken from the publication by Robert Shannon, loc. cit. According to M. Filella, P.M. May, The aqueous solution thermodynamics of niobium under con- ditions of environmental and biological interest, Applied Geochemistry 122 (2020) 104729, no Nb+5has been detected even in acidic solution at very low pH. The least hydroxylated ion is Nb(OH)4+. We therefore set the radius of a sphere volume-equivalent to Nb(OH)4+as the radius. From the quantities ΔM1, Z2, O and M determined with the help of Table 5, ΔMgesis calculated in g / mol. The prefactor f is used to convert to mg / (dm²6h). This prefactor is chosen to be the same for all glass compositions of the range according to the invention, since the glasses according tothe invention are so similar with respect to density that a detailed breakdown would not bringany significant increase in accuracy. The nominal value of f leading to the best possible agree- ment between measured and calculated values for the removal rate according to DIN 12116 is: ^= 0.0096 ∙ This results in the removal rate r: r= ^ ∙∆^ ^^^= 0.0096 ∙ For example, for a glass composed of 50% silica and 50% diboron trioxide, we first calculate thequantity ΔM1 by multiplying the numbers in the third column of table 5 by the ci and then sum-ming to 31.0824 / 2 = 15.5412. The quantity Z2 is determined by multiplying the numbers in thefourth column of table 5 by the ci and then summing up to 2.67882 / 2 = 1.33941. The quantity Ois determined by multiplying the numbers in the fifth column by the ci and then summing up to2.5. The quantity M is determined by multiplying the numbers in the sixth column by the ci andthen summing up to (60.084+69.619) / 2 = 64.8515. From Z2, O, and M, using (14), ΔM2 is deter-mined to be 34.745099046. Thus, ΔM is 50.286299046 according to (15). ε is 0.803646 accord-ing to (16). Thus, the removal rate r is 2.46 mg / (dm²6h) according to (19).15 December 2023 24 / 59 According to the invention, the removal rate is preferably at most 0.80 mg / (dm26h), more prefer-ably at most 0.75 mg / (dm26h), more preferably at most 0.70 mg / (dm26h), more preferably atmost 0.65 mg / (dm26h), particularly preferably at most 0.60 mg / (dm26h), very particularly prefer-ably at most 0.55 mg / (dm26h), most preferably at most 0.50 mg / (dm26h). What is meant is theremoval rate, which can be calculated using formula (19) for glasses of the present invention. Insome embodiments, the removal rate is at least 0.05 mg / (dm26h), for example at least 0.10 mg / (dm26h), at least 0.15 mg / (dm26h), at least 0.20 mg / (dm26h), at least 0.25 mg / (dm26h), at least 0.30 mg / (dm26h), or at least 0.35 mg / (dm26h). In some embodiments, the removal rate is in a range of from 0.05 to 0.80 mg / (dm26h), for example from 0.10 to 0.75 mg / (dm26h), from 0.15 to 0.70 mg / (dm26h), from 0.20 to 0.65 mg / (dm26h), from 0.25 to 0.60 mg / (dm26h), from 0.30 to 0.55 mg / (dm26h), or from 0.35 to 0.50 mg / (dm26h). Coefficient of thermal expansion according to ISO 7991 Surprisingly, the position of the thermal expansion coefficient according to ISO 7991 in the tar- get range can also be represented with the aid of a very simple calculation rule. This is obtained via the average bond strength. It is known from the literature that the coefficient of thermal expansion for metals, for example, is inversely proportional to the binding energy (or to the "depth of the interatomic potential wells"), see, for example, H. Föll, script for the lecture "Einführung in die MaterialwissenschaftI", Christian Albrechts- Universität Kiel, pp.79 - 83.In a simple picture of oxidic glasses, the cations are placed in a potential well formed by the sur- rounding oxygen atoms and the depth of the potential well is assumed to be the sum of the bond strengths of the various single bonds to the surrounding oxygen atoms, i.e. the entire in- teraction energy is concentrated in potential wells with the cations in the center and the oxygenatoms in the periphery. Thus, the reverse case needs no longer be considered; it would also bemore difficult to analyze, since an oxygen atom can be located between several different types of cations, which conversely cannot occur in purely oxide glasses. These values are tabulated, e.g. in DE 102014119594 A1: Table 6 CationPotential well depth / (kJ / mol)Si 1864B 1572.5Al 1537Zr 2204Nb 2298.515 December 2023 25 / 59 CationPotential well depth / (kJ / mol)Zn 728Mg 999Ca 1063Na 440.5K 395The values for Zr, Nb, and Zn are not from DE 102014119594 A1, but are calculated using ex-actly the same method described there from the values given in Standard Thermodynamic Val-ues at 25°C, retrieved from Microsoft Word - Chemistry Handbook (chemistry-reference.com)on 9 / 29 / 2021. Standard Thermodynamic Values at 25°C again gives as sources: Dean, John A. Lange's Handbook of Chemistry, 11th ed.; McGraw-Hill: New York, New York, 1979; pp 9:4- 9:128, Lide, David R. CRC Handbook, 84th ed.; CRC Press: Boca Raton, Flori-da,2003; pp 5:5- 5:60, 5:85-5:86. From the composition of a glass of the constituent phases given above, the numbers of different cations contained in the respective phases, and the potential well depths per cation tabulatedabove, a mean potential well depth can be calculated: Where m is the number of cation types occurring in each constituent phase (the numerical valueof m depends on the constituent phase), Epot,jis the potential well depth tabulated above for thej-th cation type, and zj,i is the number of cations of the j-th type in the i-th constituent phase. Thesums over j are tabulated below: Table 7 ^ Constituent Phase ∑^ ^^^ ^^,^ ∙ ^^^^,^ / ^^^,^(kJ / mol) ^^^ Reedmergnerite 1.25 1901.25Potassium-Reedmergnerite 1.25 1889.88Albite 1.25 1892.38Sodium-Zinc-Silicate 1.2 1440.2Cordierite 1.22 1940.67Vlasovite 1.16 1756.66Calcium-Zirkonium-Silicate 1 1683.57Potassium-Niobium-Silicate 1.33 2140.5Silicon Dioxide 1.00 1864.00Diboron Trioxide 2.00 3145.0015 December 2023 26 / 59 This average bond strength is inversely proportional to the coefficient of thermal expansion, as is the case for metals, see H. Föll, loc. cit. Evaluation of a number of different glasses, including commercial glasses such as Borofloat33, Borofloat40, AF45, AF32 leads to the following for- mula: 27.205^ ^^^ / ^, (21) Since the bond strength is inversely proportional to the melting point, an inverse proportionality also applies between the melting point and the coefficient of expansion, see again H. Föll, loc. cit. Since the melting point is not precisely defined for non-stoichiometric glasses, only a ten- dential relationship applies between the temperature generally referred to as the melting point, at which the viscosity is 100 dPas, and the coefficient of expansion. However, via the latter rela- tionship it is ensured that the glasses according to the invention are meltable. While the requirement for good fusibility suggests to make the coefficient of thermal expansion as high as possible, conversely the requirement for the lowest possible thermal stresses duringany thermal post-processing suggests to make the coefficient of thermal expansion as lows aspossible. The combination of both requirements leads to the middle range preferred here for thecoefficient of expansion or the mean potential well depth.The glasses of the present invention preferably have mean potential well depths of 1500 kJ / molto 1800 kJ / mol, more preferably 1515 to 1785 kJ / mol, more preferably 1530 to 1770 kJ / mol,more preferably 1538 to 1755 kJ / mol, more preferably 1561 kJ / mol to 1740 kJ / mol, more prefer-ably 1580 to 1730 kJ / mol, for example 1600 to 1715 kJ / mol, 1625 to 1700 kJ / mol, or 1640 to1660 kJ / mol. In some embodiments, the glasses have a mean potential well depth of at least1500 kJ / mol, for example at least 1515 kJ / mol, at least 1530 kJ / mol, at least 1538 kJ / mol, at least 1561 kJ / mol, at least 1580 kJ / mol, at least 1600 kJ / mol, at least 1625 kJ / mol, or at least 1640 kJ / mol. In some embodiments, the glasses have a mean potential well depth of at most 1800 kJ / mol, for example at most 1785 kJ / mol, at most 1770 kJ / mol, at most 1755 kJ / mol, atmost 1740 kJ / mol, at most 1730 kJ / mol, at most 1715 kJ / mol, at most 1700 kJ / mol, or at most1660 kJ / mol. This refers to the mean potential well depth calculated according to formula (20).According to the invention, the coefficient of thermal expansion (CTE) is preferably in a range offrom 2.50 to 6.50 ppm / K, more preferably from 2.75 to 6.25 ppm / K, such as for example from3.00 to 6.00 ppm / K, from 3.25 to 5.75 ppm / K, or from 3.50 to 5.50 ppm / K. In some embodi-ments, the CTE is at least 2.50 ppm / K, at least 2.75 ppm / K, at least 3.00 ppm / K, at least 3.25ppm / K, or at least 3.50 ppm / K. In some embodiments, the CTE is at most 6.50 ppm / K, at most15 December 2023 27 / 596.25 ppm / K, at most 6.00 ppm / K, at most 5.75 ppm / K, or at most 5.50 ppm / K. This refers to thevalue CTE, which can be calculated using formula (21) for glasses of this invention.Viscosity curve, especially working point (VA)Surprisingly, a mixing rule can also be given for viscosity of glass, with which the viscosity is cal- culated from the viscosities of the constituent phases. The starting point is the Adam-Gibbs relationship in its formulation for viscosity (see C.A. Angell, Structural Instability and Relaxation in Liquid and Glassy Phases near the fragile liiquid limit, Journal of Non-Crystalline Solids 102 (1988) 205-221): η0 is a prefactor. Q is a constant. Sc(T) is the configurational entropy, which according to Hodge is calculated from the configurational fraction ΔCp(T) of the specific heat (“excess specific heat”) under the assumption ΔCp(T) = D / T by (see C.A. Angell, loc. cit., and the literature cited there): TK is the Kauzmann temperature, which according to C.A. Angell, loc. cit., is identified with theVogel-Fulcher-Tammann temperature T0. Thus, the Adam-Gibbs relation can be transformed into the Vogel-Fulcher-Tamman equation (VFT equation): A, B, T0 are the parameters of the VFT equation, which are determined by fit to a measurement curve. With the assumptions of Angell and Hodge, Adam-Gibbs and VFT correspond to each other. Thus, the parameters η0 and D / Q, which are in the Adam-Gibbs relationship, can be calculated from the VFT parameters A, B, T0. ^= 10^^ ^^^ ∙ ^ (25a)^ ^ =^^^ (25b)15 December 2023 28 / 59 From the relationships between Adam-Gibbs and VFT, a mixing rule can be derived that can be used to calculate the VFT parameters of a glass from the VFT parameters of the constituent phases known from measurements. The first approach is: It is used here that the entropy is an additive quantity and is summed over all constituent phases. The mixture entropy is neglected according to Conradt, loc. cit.νi is the fraction of the i-th constituent phase in atom% rather than in mol%; the fact that atom%have to be used here follows from the derivation of the Adam-Gibbs equation. If in addition, one assumes that Q has one and the same value for all constituent phases as well as the glass formed by mixing them, one can calculate: The values for Di or Di / Q refer to the individual constituent phases and are obtained from theirVFT parameters Ai, Bi, T0,i according to (25). The sum over “i” is from 1 to n, as above.With B and T0, two of the three VFT parameters of the glass formed by mixing the constituent phases are known.For the determination of A, it is made use of that the VFT equation approaches an Arrheniusrelationship η = 10A+B / T dPa·s at high temperatures, and there are several literature references toan approximately linear relationship between A and B for an Arrhenius-conforming viscosity; these literature references are cited in Chen Han, Viscosity Studies of High-Temperature Metal- lurgical Slags Relevant to Ironmaking Process, PhD Thesis, School of Chemical Engineering, University of Queensland, Australia, 2017. This leads to the formula: "νi" again refers to atomic percentages. The sum over “i” is from 1 to n, as above.15 December 2023 29 / 59For the calculation of the VFT parameters of a glass expressed as a mixture of the constituentphases forming the basic system of the invention, the VFT parameters of these phases are re- quired. These are: Table 8 Constituent Phase A B / K T0 / °C T0 / KReedmergnerite -1.4233 3621.14 333.79 606.99Potassium-Reedmergnerite -2.16 4354.6 355.4 628.6Albite -5.3423 14847.05 -22.43 250.77Sodium-Zinc-Silicate -1.752 3370.6 299.9 573.1Cordierite -4.50166 6790.97 418.162 691.362Vlasovite -3.29 5450.9 521.1 794.3Calcium-Zirkonium-Silicate -4.2404008 5246.34916 542.720475 815.92Potassium-Niobium-Silicate -2.602 3824.0 459.9 733.1Silicon Dioxide -6.01651 26018.9 -240.131 33.069Diboron Trioxide -0.0871546 1650.04 149.859 423.059The VFT parameters of silica were obtained by adaptation to the measurement data of G. Ur- bain, Bottinga, P. Richet, Viscosity of liquid silica, silicates and alumino-silicates, Geochimica et Cosmochimica Acta 46 (1982), 1061-1072. All other VFT parameters were determined in the accredited measuring laboratories of Schott AG in Mainz on specially prepared test samples. For the calculations herein, T0 is used in the unit “K”. Table 8 additionally indicates T0 in the unit “°C” just as an additional information because T0 is often given in °C in the literature.If A, B, T0 are known from the formulas (27) - (28), the working point WP is calculated by trans-forming (24) according to: ^^ =^ ^^^+ ^^ (29)and the annealing point AP according to:^^ =^ ^^^^+ ^^ (30)For example, mixing the constituent phases SiO2 and B2O3 in a molar ratio of 9 : 1 or 0.9 : 0.1which is equivalent to an atomic ratio of 9*3 / (9*3+1*5) : 1*5 / (9*3+1*5) (note that SiO2 has 3 at- oms whereas B2O3 has 5 atoms), we first obtain according to equation (25b) DSiO2 / Q = (273.2- 240.131) / 26018.9 = 0.00127 and DB2O3 / Q = (273.2+149.859) / 1650.5 = 0.25632. From this, the mixture is calculated according to equation (27a) D / Q = (9*3*DSiO2 / Q +1*5*DB2O3 / Q) / (9*3+1*5) = 0.04112. From this, the T0 value of the mixture is calculated according to equation (27b) T0 = 0.04112 / ((9*3 / 26018.9+1*5 / 1650.5) / (9*3+1*5)) = 323.533 K, i.e.50.333°C. According to15 December 2023 30 / 59 equation (27c), the B value of the mixture is calculated as 323.533K / 0.04112 = 7868.03K. Ac- cording to equation (28), A = (9*3*(-6.01651) / 26018.9+1*5*(-0.0871546) / 1650.04) / ((9*3+1*5) / 7868.03) = -1.6. This gives the working point WP as (7868.03 / 5.6+323.533) K = 1728.54 K, i.e. 1455.34 °C, and the annealing point AP to(7868.03 / 14.6+323.533) K = 862.439 K, i.e.589.239 °C.According to the invention, the working point is preferably at most 1400°C, more preferably atmost 1375°C, more preferably at most 1350°C, more preferably at most 1340°C, more prefera-bly at most 1325°C, more preferably at most 1300°C, more preferably at most 1290°C, morepreferably at most 1280°C, most preferably at most 1270°C, still more preferably at most1260°C, most preferably at most 1250°C. This refers to the working point WP, which can be cal-culated using formula (29) for glasses of the invention. In some embodiments, the working point WP is at least 950°C, for example at least 975°C, at least 1000°C, at least 1025°C, at least 1050°C, at least 1075°C, at least 1100°C, at least 1125°C, at least 1150°C, at least 1175°C, or at least 1200°C. In some embodiments, the working point WP is in a range of from 950°C to 1400°C, for example from 975°C to 1375°C, from 1000°C to 1350°C, from 1025°C to 1340°C, from 1050°C to 1325°C, from 1075°C to 1300°C, from 1100°C to 1290°C, from 1125°C to 1280°C, from 1150°C to 1270°C, from 1175°C to 1260°C, or from 1200°C to 1250°C. The annealing point AP is preferably in a range of from 575°C to 900°C, for example from 600°C to 875°C, from 625°C to 850°C, from 650°C to 825°C, from 675°C to 800°C, or from 700°C to 775°C. This refers to the annealing point AP, which can be calculated using formula (30) for glasses of the invention. In some embodiments, the annealing point AP is at least 575°C, for example at least 600°C, at least 625°C, at least 650°C, at least 675°C, or at least 700°C. In some embodiments, the annealing point AP is at most 900°C, for example at most 875°C, at most 850°C, at most 825°C, at most 800°C, or at most 775°C. Selection of suitable oxides In one aspect, the present invention relates to a glass comprising the following components in the indicated amounts (in mol%): Component Min MaxSiO2 70 85ZrO2 0 5Nb2O5 0 8B2O3 0 9Al2O3 0 3ZnO 0 7MgO 0 315 December 2023 31 / 59CaO 0 8Na2O 0 8K2O 0 8In some embodiments, the glass of the invention comprises the following components in the in- dicated amounts (in mol%): Component Min MaxSiO2 75 85ZrO2 1 3Nb2O5 0 7B2O3 0 8Al2O3 0 2ZnO 0 6MgO 0 2CaO 1 6Na2O 0.5 6K2O 0 7Preferably, the sum of the amounts of ZrO2and Nb2O5is at least 1.0 mol%, and the sum of the amounts of Na2O and K2O is at least 3.0 mol%, for example at least 4.0 mol%. The glasses of the present invention comprise SiO2in a proportion of 70 to 85 mol%, for exam- ple from 73 to 84 mol%, from 74 to 83 mol%, from 75 to 82 mol%, from 76 to 81 mol%, or from 77 to 80 mol%. In some embodiments, the proportion of SiO2is at least 70 mol%, at least 73 mol%, at least 74 mol%, at least 75 mol%, at least 76 mol%, or at least 77 mol%. In some em- bodiments, the proportion of SiO2is at most 85 mol%, at most 84 mol%, at most 83 mol%, at most 82 mol%, at most 81 mol%, or at most 80 mol%. The proportion of ZrO2in the glasses of the invention is in a range of from 0 to 5.0 mol%, for ex- ample from 0.5 to 4.5 mol%, from 1.0 to 4.0 mol, from 1.2 to 3.5 mol%, or from 1.5 to 3.0 mol%. In some embodiments, the proportion of ZrO2is at least 0.5 mol%, at least 1.0 mol%, at least 1.2 mol%, or at least 1.5 mol%. In some embodiments, the proportion of ZrO2 is at most 5.0 mol%, at most 4.5 mol%, at most 4.0 mol%, at most 3.5 mol%, or at most 3.0 mol%, for exam- ple at most 2.0 mol%, or at most 1.5 mol%. In some embodiments, the glass is even free of ZrO2. The proportion of Nb2O5 in the glasses of the invention is in a range of from 0 to 8.0 mol%, for example from 0.5 to 7.0 mol%, from 1.0 to 6.0 mol%, or from 2.0 to 5.0 mol%. In some embodi- ments, the proportion of Nb2O5 is at least 0.5 mol%, at least 1.0 mol%, or at least 2.0 mol%, for example at least 5.0 mol%, or at least 6.0 mol%. In some embodiments, the proportion of Nb2O5 is at most 8.0 mol%, for example at most 7.0 mol%, at most 6.0 mol%, or at most 5.0 mol%, in15 December 2023 32 / 59 particular at most 4.0 mol%, at most 3.0 mol%, at most 2.0 mol%, or at most 1.0 mol%. In some embodiments, the glasses are free of Nb2O5. The sum of the proportions of ZrO2 and Nb2O5 is preferably in a range of from 0.5 to 12 mol%, for example from 1.0 to 10 mol%, from 1.5 to 8.0 mol%, from 2.0 to 6.0 mol%, or from 3.0 to 5.0 mol%. In some embodiments, the sum of the proportions of ZrO2and Nb2O5is at least 0.5 mol%, at least 1.0 mol%, at least 1.5 mol%, at least 2.0 mol%, or at least 3.0 mol%. In some embodiments, the sum of the proportions of ZrO2 and Nb2O5 is at most 12 mol%, at most 10mol%, at most 8.0 mol%, at most 6.0 mol%, or at most 5.0 mol%.The proportion of B2O3 in the glasses of the invention is in a range of from 0 to 9.0 mol%, for ex- ample from 3.0 to 8.5 mol%, from 5.0 to 8.0 mol%, or from 6.0 to 7.5 mol%. In some embodi- ments, the proportion of B2O3is at least 3.0 mol%, at least 4.0 mol%, at least 5.0 mol%, or at least 6.0 mol%. In some embodiments, the proportion of B2O3is at most 9.0 mol%, at most 8.5mol%, at most 8.0 mol%, at most 7.5 mol%, or at most 7.0 mol%. In some embodiments, theproportion of B2O3is at most 6.0 mol%, at most 4.0 mol%, at most 2.0 mol%, or at most 1.0 mol%, or the glasses are even free of B2O3. The proportion of Al2O3in the glasses of the invention is in a range of from 0 to 3.0 mol%, for example 0.5 to 2.0 mol%, or 1.0 to 1.5 mol%. In some embodiments, the proportion of Al2O3is at least 0.5 mol% or at least 1.0 mol%. In some embodiments, the proportion of Al2O3is at most 3.0 mol%, at most 2.5 mol%, at most 2.0 mol%, or at most 1.5 mol%, for example at most 1.0 mol%, or at most 0.5 mol%. In some embodiments, the glasses are free of Al2O3. The proportion of ZnO in the glasses of the invention is in a range of from 0 to 7.0 mol%, for ex- ample from 0.5 to 6.5 mol%, from 1.0 to 6.0 mol%, or from 1.5 to 5.5 mol%. In some embodi-ments, the proportion of ZnO is at least 0.5 mol%, at least 1.0 mol%, at least 1.5 mol%, at least2.0 mol%, at least 3.0 mol%, at least 4.0 mol%, or at least 5.0 mol%. In some embodiments, the proportion of ZnO is at most 7.0 mol%, at most 6.5 mol%, at most 6.0 mol%, at most 5.5 mol%,at most 5.0 mol%, at most 4.0 mol%, at most 3.0 mol%, or at most 1.0 mol%. In some embodi-ments, the glasses are free of ZnO. The proportion of MgO in the glasses of the invention is in a range of from 0 to 3.0 mol%, for ex- ample from 0.5 to 2.0 mol%, or from 1.0 to 1.5 mol%. In some embodiments, the proportion ofMgO is at least 0.5 mol% or at least 1.0 mol%. In some embodiments, the proportion of MgO isat most 3.0 mol%, at most 2.5 mol%, at most 2.0 mol%, or at most 1.5 mol%, for example at most 1.0 mol%, or at most 0.5 mol%. In some embodiments, the glasses are free of MgO.15 December 2023 33 / 59 The proportion of CaO in the glasses of the invention is in a range of from 0 to 8.0 mol%, for ex- ample from 0.5 to 7.0 mol%, from 1.0 to 6.0 mol%, or from 2.0 to 5.0 mol%. In some embodi- ments, the proportion of CaO is at least 0.5 mol%, at least 1.0 mol%, at least 1.5 mol%, at least 2.0 mol%, or at least 2.5 mol%. In some embodiments, the proportion of CaO is at most 8.0 mol%, at most 7.0 mol%, at most 6.0 mol%, or at most 5.0 mol%, for example at most 4.0 mol%, at most 3.0 mol%, at most 2.0 mol%, or at most 1.0 mol%. In some embodiments, the glasses are free of CaO. The proportion of Na2O in the glasses of the invention is in a range of from 0 to 8.0 mol%, forexample from 0.5 to 7.5 mol%, from 1.0 to 7.0 mol%, from 2.0 to 6.5 mol%, or from 3.0 to 6.0mol%, or from 4.0 to 5.0 mol%. In some embodiments, the proportion of Na2O is at least 0.5 mol%, at least 1.0 mol%, at least 2.0 mol%, at least 3.0 mol%, or at least 4.0 mol%. In some embodiments, the proportion of Na2O is at most 8.0 mol%, at most 7.5 mol%, at most 7.0 mol%, at most 6.5 mol%, at most 6.0 mol%, or at most 5.0 mol%, for example at most 3.0 mol%, or at most 1.0 mol%. In some embodiments, the glasses are free of Na2O. The proportion of K2O in the glasses of the invention is in a range of from 0 to 8.0 mol%, for ex- ample from 0.1 to 7.0 mol%, from 0.2 to 6.0 mol%, from 0.5 to 5.0 mol%, from 1.0 to 4.0 mol%, or from 2.0 to 3.0 mol%. In some embodiments, the proportion of K2O is at least 0.1 mol%, at least 0.2 mol%, at least 0.5 mol%, at least 1.0 mol%, or at least 2.0 mol%. In some embodi- ments, the proportion of K2O is at most 8.0 mol%, at most 7.0 mol%, at most 6.0 mol%, at most 5.0 mol%, at most 4.0 mol%, or at most 3.0 mol%, for example at most 2.0 mol% or at most 1.0 mol%. In some embodiments, the glasses are free of K2O. The sum of the proportions of Na2O and K2O is preferably in a range of from 3.0 to 12 mol%, for example from 4.0 to 10 mol%, from 5.0 to 9.0 mol%, from 6.0 to 8.0 mol%, or from 6.5 to 7.5 mol%. In some embodiments, the sum of the proportions of Na2O and K2O is at least 3.0 mol%, at least 4.0 mol%, at least 5.0 mol%, at least 6.0 mol%, or at least 6.5 mol%. In some embodi- ments, the sum of the proportions of Na2O and K2O is at most 12 mol%, at most 10 mol%, at most 9.0 mol%, at most 8.0 mol%, or at most 7.5 mol%. The ratio of the sum of the proportions of Na2O and K2O to the sum of the proportions of ZrO2 and Nb2O5 is preferably in a range of from 0.5 to 6.0, for example from >1.0 to 3.0, or from 1.5 to 2.5. In some embodiments, the ratio of the sum of the proportions of Na2O and K2O to the sum of the proportions of ZrO2 and Nb2O5 is at least 0.5, at least >1.0, or at least 1.5. It is partic- ularly preferred that the sum of the proportions of Na2O and K2O is higher than the sum of theproportions of ZrO2 and Nb2O5. In some embodiments, the ratio of the sum of the proportions of15 December 2023 34 / 59 Na2O and K2O to the sum of the proportions of ZrO2 and Nb2O5 is at most 6.0, at most 3.0, or at most 2.5. Selection of suitable constituent phases Reedmergnerite In terms of alkali, hydrolytic and acid resistance, Reedmergnerite (American Mineralogist, Vol-ume 50, pages 1827-1850, 1965) is selected as constituent phase. Reedmergnerite has a lownumber of 3D angular degrees of freedom per atom, which is advantageous for alkali re- sistance. It consists of 75 mol% SiO2 and 12.5 mol% Na2O, resulting in a buffer solution in water as described above. Its pH is lowered by the additional 12.5 mol% of B2O3 (relative to additional SiO2). This is beneficial for hydrolytic stability. The composition of silicon and boron, both of which do not release their hydroxyl groups in aqueous solution even at the lowest pH values and are therefore difficult to move, and relatively large (radius > 1 Å) sodium ions is advanta- geous for acid resistance.Because of its annealing point of 585°C and its working point of 1002°C, reedmergnerite is ide-ally suited as an easily fusible basic system for the glasses of the invention. According to the invention, one mole of reedmergnerite is understood to be one mole of (Na2O·B2O3·6SiO2) / 8. In some embodiments, the proportion of reedmergnerite is in a range of from 0 to 50 mol%, forexample from 5.0 to 45 mol%, from 10 to 40 mol%, from 11 to 38 mol%, from 12 to 36 mol%, orfrom 15 to 35 mol%. In some embodiments, the proportion of reedmergnerite is at least 5.0mol%, at least 10 mol%, at least 11 mol%, at least 12 mol%, or at least 15 mol%. In some em-bodiments, the proportion of reedmergnerite is at most 50 mol%, at most 45 mol%, at most 40mol%, at most 38 mol%, at most 36 mol%, or at most 35 mol%, for example at most 20 mol% orat most 10 mol%. In some embodiments, the glasses are free of reedmergnerite. Potassium-Reedmergnerite To suppress a possible tendency to demixing, the potassium analogue of reedmergnerite isadded as a constituent phase (Mineralogical Magazine 57 (1993) 157-164). Regarding thechemical stability potassium reedmergnerite is comparable to reedmergnerite.15 December 2023 35 / 59Because of its annealing point of 643°C and its working point of 1062°C, potassium-reed-mergnerite is suitable as an easily fusible basic system for the glasses according to the inven- tion. One mole of potassium-reedmergnerite is understood to be one mole of (K2O·B2O3·6SiO2) / 8. The proportion of potassium-reedmergnerite is preferably in a range of from 0 to 25 mol%, for example from 0.5 to 20 mol%, from 1.0 to 15 mol%, or from 2.0 to 10 mol%. In some embodi- ments, the proportion of potassium-reedmergnerite is at least 0.5 mol%, at least, 1.0 mol%, or at least 2.0 mol%. In some embodiments, the proportion of potassium-reedmergnerite is at most 25 mol%, at most 20 mol%, at most 19 mol%, at most 18 mol%, at most 15 mol%, or at most 10 mol%, for example at most 5.0 mol%. In some embodiments, the glasses are free of potassium- reedmergnerite. AlbiteTo further suppress a possible demixing tendency of a pure borosilicate system, the aluminumanalogue of reedmergnerite, albite, is added as a constituent phase (American Mineralogist,Volume 81, pages 1344-1349, 1996), see on the segregation issue J.W. Greig, Immiscibility in silicate melts, Am. J. Sci., 5th ser., Vol.13 (1927), 1-44 and 133-154. Furthermore, a certain amount of albite increases the chemical toughness of the glasses. However, compared to reed- mergnerite, albite has a much higher number of 3D angular degrees of freedom per atom, and the aluminum ions formed in the acidic environment are very mobile because of their small size (radius about 0.5 Å). These two circumstances are unfavorable for alkali and acid resistance, so that the albite content should be limited upward. The pH resulting from dissolving the glass in neutral water is higher than that resulting from dissolving an equal amount of reedmergnerite because aluminum is an amphoteric and not an acid generator like boron. This is unfavorable for hydrolytic resistance. Albite is not suitable as an easily fusible base system for the glasses of the invention becauseof its annealing point of 787°C and its working point of 1567°C.According to the invention, one mole of albite is understood to be one mole of (Na2O∙Al2O3∙6SiO2) / 8. The proportion of albite is preferably in a range of from 0 to 15 mol%, for example from 0.1 to 10 mol%, from 0.5 to 5.0 mol%, or from 1.0 to 2.0 mol%. In some embodiments, the proportion of albite is at least 0.1 mol%, at least 0.5 mol%, or at least 1.0 mol%. In some embodiments, the proportion of albite is at most 15 mol%, at most 10 mol%, at most 5.0 mol%, or at most 2.015 December 2023 36 / 59 mol%, for example at most 1.0 mol% or at most 0.5 mol%. Preferably, the glasses are free of albite. Sodium-Zinc-Silicate Like the first three constituent phases, sodium-zinc-silicate consists of network converters (so- dium), intermediate ions (zinc) and network formers (silicon). In contrast to albite, for example, sodium-zinc-silicate has only one intermediate ion, which also has only the valence "2". Both are advantageous for acid resistance. Intermediate ions of high valence such as aluminum ("3") have a small ionic radius, which makes them very mobile and allows them to leave the glass network quickly in the acid resistance test, and are replaced by many (in the case of aluminum again "3") hydroxyl ions in the acid resistance test, which greatly weakens the network.Because of its annealing point of 529°C and its working point of 902°C, sodium-zinc-silicate isexcellently suited as an easily meltable basic system for the glasses according to the invention. According to the invention, one mole of sodium zinc silicate is understood to be one mole of (Na2O·ZnO·3SiO2) / 5. The proportion of sodium-zinc-silicate is preferably in a range of from 0 to 35 mol%, for example from 1.0 to 30 mol%, from 1.5 to 28 mol%, from 2.0 to 25 mol%, from 5.0 to 20 mol%, or from 7.5 to 15 mol%. In some embodiments, the proportion of sodium-zinc-silicate is at least 1.0 mol%, at least 1.5 mol%, at least 2.0 mol%, at least 5.0 mol%, or at least 7.5 mol%. In someembodiments, the proportion of sodium-zinc-silicate is at most 35 mol%, at most 30 mol%, atmost 29 mol%, at most 28 mol%, at most 25 mol%, at most 20 mol%, or at most 15 mol%, forexample at most 10 mol% or at most 5.0 mol%. In some embodiments, the glasses are free of sodium-zinc-silicate. Cordierite All constituent phases mentioned so far are alkali-containing. Depending on the alkali content, alkali-containing glasses have higher expansion coefficients (e.g.8 to 10 ppm / K) than preferred in the invention. To compensate, phases are added whose contribution either pushes the ex- pansion coefficient far down (SiO2, B2O3) or shifts it to medium values, e.g. cordierite as an alu- minosilicate of an alkaline earth. Due to the relatively high alkaline earth content, cordierite lowers the alkali and hydrolytic re- sistance in relation to the first three constituent phases. Due to its high aluminum content,15 December 2023 37 / 59 cordierite behaves particularly unfavorably with regard to acid resistance, so that the cordierite content must be limited.Because of its annealing point of 806°C and its working point of 1217°C, cordierite is not ideallysuited as an easily fusible base system for the glasses of the invention. One mole of cordierite is understood to mean one mole of (2MgO∙2Al2O3∙5SiO2) / 9. The proportion of cordierite is preferably in a range of from 0 to 15 mol%, for example from 0.1 to 10 mol%, from 0.2 to 8.0 mol%, from 0.5 to 5.0 mol%, or from 1.0 to 4.0 mol%. In some em-bodiments, the proportion of cordierite is at least 0.1 mol%, at least 0.2 mol%, at least 0.5mol%, or at least 1.0 mol%. In some embodiments, the proportion of cordierite is at most 15 mol%, at most 10 mol%, at most 8.0 mol%, at most 6.0 mol%, at most 5.0 mol%, or at most 4.0mol%, for example at most 2.0 mol%, or at most 1.0 mol%. In some embodiments, the glassesare free of cordierite. VlasoviteVlasovite is a zirconium-containing phase which, due to the dense packing of the zirconium ionand its environment, provides hardly any space for a penetrating hydroxyl ion, which has an ex- tremely advantageous effect on the alkali resistance. It is not so advantageous with regard to hydrolytic and acid resistance (Zr+4is a small ion of high valence, which according to the above- mentioned considerations, which are also experimentally confirmed with vlasovite, is unfavora- ble for acid resistance), so that it is sensibly combined with other phases.Because of its very high annealing point of 856°C and its working point of 1269°C, vlasovite isnot suitable as an easily melted and handled basic system for the glasses of the invention.One mole of vlasovite is understood to be one mole of (Na2O∙ZrO2∙4SiO2) / 6.The proportion of vlasovite is preferably in a range of from 0 to 30 mol%, for example from 0.1to 20 mol%, from 0.2 to 15 mol%, from 0.5 to 10 mol%, or from 1.0 to 5.0 mol%. In some em-bodiments, the proportion of vlasovite is at least 0.1 mol%, at least 0.2 mol%, at least 0.5 mol%, or at least 1.0 mol%, for example at least 5.0 mol%, or at least 10 mol%. In some embodiments, the proportion of vlasovite is at most 30 mol%, at most 20 mol%, at most 15 mol%, at most 12 mol%, at most 11 mol%, at most 10 mol%, or at most 5.0 mol%, for example at most 2 mol%, or at most 1 mol%. In some embodiments, the glasses of the invention are free of vlasovite.15 December 2023 38 / 59 Calcium-Zirconium-Silicate Calcium-zirconium-silicate is a zirconium-containing phase which, like vlasovite, offers hardly any space for penetrating hydroxyl ions because of the dense packing of the zirconium ion and its environment, which has an extremely advantageous effect on the alkali resistance. It is not so advantageous with regard to acid resistance (Zr+4is a small ion of high valence, which ac- cording to the above considerations, which are also experimentally confirmed by vlasovite, is unfavorable for acid resistance, Ca++is also smaller than e.g. Na+and has a higher valence), so that it is sensibly combined with other phases. Calcium zirconium silicate is not suitable as an easily melted and handled base system for theglasses of the invention because of its very high annealing point of 846°C and its working pointof 1194°C. By one mole of calcium-zirconium-silicate is meant one mole of (2CaO∙ZrO2∙4SiO2) / 7. The proportion of calcium-zirconium-silicate is preferably in a range of from 0 to 30 mol%, forexample from 2.0 to 25 mol%, from 4.0 to 22 mol%, from 5.0 to 21 mol%, from 10 to 20 mol%,or from 12 to 15 mol%. In some embodiments, the proportion of calcium-zirconium-silicate is at least 1.0 mol%, at least 2.0 mol%, at least 4.0 mol%, at least 5.0 mol%, at least 7.5 mol%, at least 10 mol%, or at least 12 mol%. In some embodiments, the proportion of calcium-zirconium- silicate is at most 30 mol%, at most 25 mol%, at most 22 mol%, at most 21 mol%, at most 20 mol%, or at most 15 mol%, for example at most 10 mol%, or at most 5.0 mol%. In some embod- iments, the glasses are free of calcium-zirconium-silicate. Potassium-Niobium-Silicate Potassium-niobium-silicate is a phase which, like vlasovite, offers little space for a penetrating hydroxyl ion due to the dense packing of the niobium ion and its environment, which has an ad- vantageous effect on the alkali resistance, even if the effect is not as pronounced as with vlaso- vite. On the other hand, it is somewhat more advantageous in terms of acid resistance. Nb+5, like Zr+4, is a small ion of high valence, but it aggregates with hydroxyl groups (Nb(OH)4+) even at very low pH values, which limits its mobility. Acceptable values for acid resistance are ob- tained when it is combined with SiO2.Because of its annealing point of 705°C and its working point of 1039°C, potassium-niobium-silicate is well suited as an easily fusible basic system for the glasses according to the invention and thus an interesting alternative to reedmergnerite, which can serve as a basis for a com- pletely boron-free neutral glass.15 December 2023 39 / 59 One mole of potassium-niobium-silicate is understood to mean one mole of (K2O∙Nb2O5∙4SiO2) / 6. The proportion of potassium-niobium-silicate is preferably in a range of from 0 to 50 mol%, for example from 1.0 to 45 mol%, from 1.5 to 42 mol%, from 2.0 to 30 mol%, from 5.0 to 20 mol%, or from 10 to 15 mol%. In some embodiments, the proportion of potassium-niobium-silicate is at least 1.0 mol%, at least 1.5 mol%, at least 2.0 mol%, at least 5.0 mol%, or at least 10 mol%. In some embodiments, the proportion of potassium-niobium-silicate is at most 50 mol%, at most 45 mol%, at most 42 mol%, at most 41 mol%, at most 30 mol%, at most 20 mol%, or at most 15 mol%, for example at most 10 mol%, or at most 5.0 mol%. In some embodiments, the glasses are free of potassium-niobium-silicate. The sum of the proportions of vlasovite, calcium-zirconium-silicate and potassium-niobium-sili-cate is preferably in a range of from 5.0 to 70 mol%, for example from 7.5 to 65 mol%, from 10to 55 mol%, from 12 to 45 mol%, from 15 to 35 mol%, or from 20 to 30 mol%. In some embodi- ments, the sum of the proportions of vlasovite, calcium-zirconium-silicate and potassium-nio- bium-silicate is at least 5.0 mol%, at least 7.5 mol%, at least 10 mol%, at least 12 mol%, at least 15 mol%, or at least 20 mol%. In some embodiments, the sum of the proportions of vlasovite, calcium-zirconium-silicate and potassium-niobium-silicate is at most 70 mol%, at most 65 mol%, at most 55 mol%, at most 45 mol%, at most 35 mol%, or at most 30 mol%. SiO2, B2O3To begin with, SiO2, B2O3 are suitable to push down the coefficient of expansion and thus, on balance, to desired values. Silicon dioxide increases the alkali resistance, but not as much as the zirconium-containing phases, lowers the pH in the aqueous solution in the hydrolytic resistance test, and makes the greatest contribution to increasing the acid resistance.With regard to the annealing point (1128°C) and the working point (2357°C), it is unsuitable asan easily meltable basic system for the glasses according to the invention, only as an admix- ture. The proportion of silicon dioxide is preferably in a range of from 15 to 60 mol%, for examplefrom 20 to 55 mol%, from 25 to 52 mol%, from 30 to 50 mol%, or from 35 to 45 mol%. In someembodiments, the proportion of silicon dioxide is at least 15 mol%, at least 20 mol%, at least 25 mol%, at least 30 mol%, or at least 35 mol%. In some embodiments, the proportion of silicon15 December 2023 40 / 59dioxide is at most 60 mol%, at most 55 mol%, at most 52 mol%, at most 50 mol%, or at most 45mol%. Diboron trioxide forms boroxol rings as a constituent phase, which have a favorable effect on the mechanical properties, see Christian Hermansen, Qantitative Evaluation of Densification and Crack Resistance in Silicate Glasses, Master Thesis, Aalborg University, Denmark, 2011. However, the resulting disruption of the network leads to greater mobility of penetrating hydroxyl ions and thus to a drastic reduction in the alkali resistance. The lowering of pH in the aqueoussolution during hydrolytic resistance testing is favourable with respect to chemical resistance;this effect is even greater than that caused by SiO2. However, pure diboron trioxide is hygro- scopic. Diboron trioxide lowers the acid resistance. There is another reason to introduce diboron trioxide as a constituent phase in the glass. This shifts the boron / sodium ratio to higher values, which lowers sodium and boron evaporation dur- ing melting and hot forming, see in C. Pentzel, D. Höhne, Chemische Aspekte bei Verdamp- fungsvorgängen aus Borosilicatglasschmelzen, Teil III, Sprechsaal 124 (1991), 327-329. In view of the above-mentioned hygroscopy alone, diboron trioxide is unsuitable as a basic sys- tem for the glasses according to the invention, only as an admixture. The proportion of diboron trioxide is preferably in a range of from 0 to 10 mol%, for example from 0.1 to 5.0 mol%, from 0.2 to 3.0 mol%, or from 0.5 to 1.5 mol%. In some embodiments, the proportion of diboron trioxide is at least 0.1 mol%, at least 0.2 mol%, or at least 0.5 mol%. Insome embodiments, the proportion of diboron trioxide is at most 10 mol%, at most 5.0 mol%, atmost 4.0 mol%, at most 3.0 mol%, or at most 1.5 mol%. In some embodiments, the glasses arefree of diboron trioxide. Further components In addition to the components already mentioned, the glass may contain further constituents,referred to herein as "balance". The proportion of balance in the glass according to the inventionis preferably at most 5 mol-%, so as not to disturb the glass properties set by careful selectionof suitable base glasses. In particularly preferred embodiments, the proportion of balance in theglass is at most 3 mol%, more preferably at most 2 mol% or at most 1 mol% or at most 0.5mol%. The balance contains in particular oxides which are not contained in the base glassesmentioned herein. Thus, the balance in particular does not contain SiO2, B2O3, Al2O3, ZnO,MgO, ZrO2, CaO, Nb2O5, Na2O or K2O. According to the invention, additions of further simple oxides of so-called "intermediates", i.e. oxides which stand between the network formers suchas SiO2 and the network converters such as Na2O, are optionally used as the balance (see15 December 2023 41 / 59Journal of The American Ceramic Society Vol.30, No. 9 (1947), pp. 277 - 281). Although theseoxides do not form glasses on their own, they can be incorporated into the network in the afore-mentioned percentage range. Thus, the balance may contain, in particular, oxides such as TiO2.According to the theory of A. Dietzel, Die Kationenfeldstärken und ihre Beziehungen zu Entglasungsvorgängen, zur Verbindungsbildung und zu den Schmelzpunkten von Silicaten, Berichte der Bunsengesellschaft für physikalische Chemie Vol.48 Nr.1 (1942), 9-23, Ta2O5 alsobelongs to the "intermediates", as can be calculated using the ionic radii according to R. Shan-non, Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides, Acta Cryst. (1976) A32, 751-767. When this description states that the glasses are free of a component or constituent phase or do not contain a certain component or constituent phase, it is meant that this component or con- stituent phase may be present at most as an impurity in the glasses. This means that it is not added in substantial amounts. According to the invention, non-substantial amounts are amountsof less than 500 ppm (molar), preferably less than 300 ppm (molar), particularly preferably lessthan 100 ppm (molar), even more preferably less than 50 ppm (molar), and most preferably less than 10 ppm (molar). In particular, the glasses of the present invention are free of lithium, lead, arsenic, antimony, bismuth and / or cadmium. Preferred glass compositions In a preferred embodiment, the glass according to the invention is characterized by the following preferred and particularly preferred proportions of constituent phases in the base glass compo-sition. The preferred ranges of proportions and further features with respect to the glass accord-ing to the invention set out above and below also apply to the preferred and particularly pre- ferred embodiment outlined below: Table 9 preferred more preferredConstituent Phase Min (Mol%) Max (Mol%) Min (Mol%) Max (Mol%)Reedmergnerite 0 38 0 36Potassium-Reedmergne-0 19 0 18rite Albite 0 2 0 115 December 2023 42 / 59preferred more preferredConstituent Phase Min (Mol%) Max (Mol%) Min (Mol%) Max (Mol%)Sodium-Zinc-Silicate 0 29 0 28Cordierite 0 8 0 6Vlasovite 0 12 0 11Calcium-Zirkonium-Sili-2 22 4 21cate Potassium-Niobium-Sili-0 42 0 41cate Silicon Dioxide 25 52 30 51Diboron Trioxide 0 4 0 3optional balance 0 5 0 5ProductionAlso, according to the invention is a method for producing a glass of the present invention, com-prising the steps of:- Melting the glass raw materials,- optionally forming a glass article, in particular a glass tube, from the molten glass- Cooling of the glass.Forming the glass may comprise a drawing process, in particular a tube drawing process. Cool- ing may involve active cooling using a coolant, such as a cooling fluid, or passive cooling. Uses and glass articles According to the invention, in addition to the glass, glass articles formed from the glass include glass tubes and containers (such as bottles, ampoules, cartridges, syringes). Preferably, the glass articles are intended for use as packaging materials for pharmaceutical products, in partic- ular as containers for liquids. In the context of these uses, hydrolytic and alkali resistance are of particular interest.15 December 2023 43 / 59

[0002] 15 December 2023 44 / 59 Examples Conversion from composition of constituent phases to composition of simple ox- ides and vice versa For comparison with the prior art, we first give a conversion matrix for the mutual conversion of both compositional data. The composition in constituent phases is given in the following normalized form for the purpose of conversion: Table 10 Constituent Phase Formula (normalizedto a simple oxide) Reedmergnerite (Na2O∙B2O3∙6SiO2) / 8Potassium-Reedmergne- (K2O∙B2O3∙6SiO2) / 8 rite Albite (Na2O∙Al2O3∙6SiO2) / 8Sodium-Zinc-Silicate (Na2O∙ZnO∙3SiO2) / 5Cordierite (2MgO∙2Al2O3∙5SiO2) / 9Vlasovite (Na2O∙ZrO2∙4SiO2) / 6Calcium-Zirkonium-Silicate (2CaO∙ZrO2∙4SiO2) / 7Potassium-Niobium-Sili- (K2O∙Nb2O5∙4SiO2) / 6 cate Silicon Dioxide SiO2Diboron Trioxide B2O3The conversion of these compositions into a composition statement in mol% with respect to thefollowing simple oxides …15 December 2023 45 / 59# Oxid1. SiO22. ZrO23. Nb2O54. B2O35. Al2O36. ZnO7. MgO8. CaO9. Na2O10. K2O… is carried out with the aid of the matrix given here. The composition in mol% with respect to the constituent phases is multiplied as a column vector from the right to the matrix: Matrix 6 / 8 6 / 8 6 / 8 3 / 5 5 / 9 4 / 6 4 / 7 4 / 6 1 00 0 0 0 0 1 / 6 1 / 7 0 0 00 0 0 0 0 0 0 1 / 6 0 01 / 8 1 / 8 0 0 0 0 0 0 0 10 0 1 / 8 0 2 / 9 0 0 0 0 00 0 0 1 / 5 0 0 0 0 0 00 0 0 0 2 / 9 0 0 0 0 00 0 0 0 0 0 2 / 7 0 0 01 / 8 0 1 / 8 1 / 5 0 1 / 6 0 0 0 00 1 / 8 0 0 0 0 0 1 / 6 0 0As a result of the multiplication of the column vector to the matrix, the composition of the glass in mole percent is obtained.15 December 2023 46 / 59 Conversely, a composition in mole percent can easily be converted via the respective inverse matrix into a glass composition given in constituent phases. Of course, only glass compositions which do not give negative values for the constituent phases when converted are considered to be according to the invention. Examples The examples are listed below. Table 11 Proportion in Mol%Example Number 1 2 3 4 5 6 7 8 9 10Reedmergnerite 45 45 45 45 40 35 25 20 20 15Potassium-Reedmerg-10 10 10 10 10 10 5 10 10 0nerite Albite 10 0 0 0 0 0 0 5 5 0Sodium-Zinc-Silicate 0 0 0 0 0 0 0 0 0 0Cordierite 0 5 0 0 0 0 0 0 0 10Vlasovite 0 0 10 0 0 0 10 20 10 0Calcium-Zirconium-Sili-10 10 10 10 10 10 10 10 10 10cate Potassium-Niobium-Si-0 0 0 14 10 10 10 0 10 20licate Silicon Dioxide 25 30 25 21 30 33 38 30 33 43Diboron Trioxide 0 0 0 0 0 2 2 5 2 2Calculated Properties CTE / (ppm / K) 5.04 4.63 5.02 5.0 4.52 4.33 4.0 4.69 4.33 3.39Removal rate ISO 695 / 57.5 55.6 45.4 60.7 56.5 67.8 52.9 61.1 56 67.7(mg / (dm²3h)) pH (50 µmol / l H2O) 8.70 8.70 8.69 8.75 8.7 8.66 8.62 8.59 8.66 8.70Removal rate DIN 12116 0.38 0.36 0.35 0. 39 0.32 0.34 0.39 0.55 0.45 0.58Annealing point / °C 669 674 678 664 679 654 692 645 693 715Working point / °C 1191 1185 1169 1118 1171 1149 1207 1150 1203 1230Table 12 Proportion in Mol%Example Number 11 12 13 14 15 16 17 18 19 20Reedmergnerite 30 32 32 40 40 35 40 35 40 36Potassium-Reedmerg-10 10 10 10 15 15 15 15 20 16nerite Albite 0 0 0 0 0 10 10 10 0 015 December 2023 47 / 59Proportion in Mol%Example Number 11 12 13 14 15 16 17 18 19 20Sodium-Zinc-Silicate 5 0 5 5 0 0 0 0 0 4Cordierite 5 5 0 5 5 0 0 5 5 0Vlasovite 0 0 0 0 0 0 0 0 0 0Calcium-Zirconium-Sili-22 25 25 10 15 15 10 10 10 16cate Potassium-Niobium-Sili-0 0 0 0 0 0 0 0 0 0cate Silicon Dioxide 25 25 25 28 23 23 24 24 24 27Diboron Trioxide 3 3 3 2 2 2 1 1 1 1Calculated Properties CTE / (ppm / K) 4.87 4.45 4.85 5.07 4.91 5.00 5.10 5.03 5.02 4.97Removal rate ISO 695 / 68.5 64.5 64.5 70.5 67.6 67.6 64.7 66.2 65.4 58.7(mg / (dm²3h)) pH (50 µmol / l H2O) 8.80 8.76 8.79 8.74 8.73 8.72 8.70 8.73 8.71 8.75Removal rate DIN 12116 0.60 0.59 0.48 0.45 0.49 0.47 0.41 0.53 0.42 0.35Annealing point / °C 640 651 637 633 642 648 654 666 651 656Working point / °C 1105 1117 1099 1124 1113 1148 1167 1179 1135 1142Table 13Proportion in Mol%Example Number 21 22 23 24 25 26 27 28 29 30Reedmergnerite 30 27 27 30 30 30 35 35 35 35Potassium-Reedmerg-10 8 8 15 15 18 18 18 18 18nerite Albite 0 0 0 0 0 0 0 10 9 9Sodium-Zinc-Silicate 0 0 2 0 0 0 0 0 0 0Cordierite 5 5 5 5 5 5 5 0 0 0Vlasovite 0 0 0 0 0 0 0 0 0 0Calcium-Zirconium-Sili-22 25 20 12 15 12 10 10 10 11cate Potassium-Niobium-Sili-0 0 0 0 0 0 0 0 0 0cate Silicon Dioxide 30 32 35 36 33 33 31 26 27 26Diboron Trioxide 3 3 3 2 2 2 1 1 1 1Calculated Properties CTE / (ppm / K) 4.24 4.00 4.11 4.20 4.29 4.39 4.58 4.98 4.92 4.95Removal rate ISO 695 / 64.9 61.5 64.9 64.8 63.6 66.5 62.4 64.4 63.9 63.5(mg / (dm²3h)) pH (50 µmol / l H2O) 8.73 8.73 8.71 8.65 8.68 8.67 8.68 8.69 8.68 8.6915 December 2023 48 / 59Proportion in Mol%Example Number 21 22 23 24 25 26 27 28 29 30Removal rate DIN 12116 0.52 0.54 0.48 0.38 0.42 0.4 0.38 0.39 0.38 0.39Annealing point / °C 658 670 662 666 661 661 668 663 664 664Working point / °C 1148 1165 1172 1194 1176 1176 1180 1186 1188 1183Table 14 Proportion in Mol%Example Number 31 32 33 34 35 36 37 38 39 40Reedmergnerite 0 0 0 0 0 0 0 0 0 0Potassium-Reedmerg-0 0 0 0 0 0 0 0 0 0nerite Albite 0 0 0 0 0 0 0 5 0 0Sodium-Zinc-Silicate 0 0 0 0 0 0 0 0 10 12Cordierite 0 0 0 0 0 0 5 0 0 0Vlasovite 25 20 10 15 5 10 5 5 10 10Calcium-Zirconium-Sili-0 0 10 0 10 5 5 5 10 8cate Potassium-Niobium-Sili-40 45 40 45 40 40 40 40 20 20cate Silicon Dioxide 35 35 40 40 45 45 45 45 50 50Diboron Trioxide 0 0 0 0 0 0 0 0 0 0Calculated Properties CTE / (ppm / K) 3.97 3.89 3.36 3.60 3.07 3.22 3.16 3.24 3.69 3.88Removal rate ISO 695 / 38.7 44.1 45.4 47.5 49 47 54 53.3 41.7 43.4(mg / (dm²3h)) pH (50 µmol / l H2O) 8.71 8.73 8.75 8.71 8.73 8.69 8.73 8.70 8.76 8.77Removal rate DIN 12116 0.55 0.55 0.49 0.48 0.43 0.42 0.51 0.44 0.36 0.35Annealing point / °C 788 778 788 780 790 791 789 789 789 779Working point / °C 1254 1237 1261 1255 1281 1287 1284 1299 1335 1326Table 15Proportion in Mol%Example Number 41 42 43 44 45 46 47 48 49 50Reedmergnerite 0 0 0 0 0 0 0 0 0 0Potassium-Reedmerg-0 0 0 0 0 0 0 0 0 0nerite Albite 0 0 0 0 0 0 0 0 0 0Sodium-Zinc-Silicate 18 18 16 17 0 5 10 0 0 6Cordierite 0 0 0 0 0 0 0 0 0 0Vlasovite 0 0 0 0 0 0 0 5 5 015 December 2023 49 / 59Proportion in Mol%Example Number 41 42 43 44 45 46 47 48 49 50Calcium-Zirconium-Sili-16 18 20 19 10 10 10 5 10 10cate Potassium-Niobium-Sili-16 16 16 16 40 35 30 40 35 32cate Silicon Dioxide 50 48 48 48 50 50 50 50 50 52Diboron Trioxide 0 0 0 0 0 0 0 0 0 0Calculated Properties CTE / (ppm / K) 4.08 4.15 3.95 4.05 2.77 3.14 3.53 2.93 2.84 3.13Removal rate ISO 695 / 49.4 48.7 46.8 47.8 52.7 53.4 54 50.6 46.4 52.4(mg / (dm²3h)) pH (50 µmol / l H2O) 8.86 8.88 8.87 8.88 8.70 8.75 8.79 8.67 8.68 8.74Removal rate DIN 12116 0.35 0.37 0.38 0.38 0.37 0.36 0.36 0.37 0.37 0.34Annealing point / °C 755 754 764 759 793 780 766 794 806 783Working point / °C 1296 1284 1292 1288 1302 1296 1289 1311 1327 1316Table 16 Proportion in Mol%Example Number 51 52 53 54 55 56 57 58 59 60Reedmergnerite 0 0 0 0 0 0 0 0 0 0Potassium-Reedmerg-0 0 0 0 0 0 0 0 0 0nerite Albite 0 0 0 0 0 0 0 0 0 0Sodium-Zinc-Silicate 25 25 25 25 30 30 25 30 28 10Cordierite 10 5 0 0 0 5 5 5 6 0Vlasovite 0 0 0 0 0 0 0 0 0 0Calcium-Zirconium-Sili-10 10 10 15 20 15 20 20 20 0cate Potassium-Niobium-Sili-10 15 15 15 5 5 5 0 0 45cate Silicon Dioxide 45 45 50 45 45 45 45 45 46 45Diboron Trioxide 0 0 0 0 0 0 0 0 0 0Calculated Properties CTE / (ppm / K) 5.05 5.02 4.77 4.94 5.33 5.41 4.89 5.35 5.12 3.91Removal rate ISO 695 / 59 58.8 55.4 53.5 49.1 54 49.2 49.3 48.8 66.7(mg / (dm²3h)) pH (50 µmol / l H2O) 8.95 8.94 8.90 8.93 8.97 8.97 8.95 8.98 8.96 8.81Removal rate DIN 12116 0.59 0.48 0.34 0.40 0.40 0.48 0.49 0.49 0.50 0.41Annealing point / °C 728 722 725 723 716 713 737 721 731 739Working point / °C 1264 1247 1273 1239 1244 1248 1269 1262 1278 122515 December 2023 50 / 59 Table 17 Proportion in Mol%Example Number 61 62 63 64 65 66 67 68 69 70Reedmergnerite 0 0 0 0 0 0 0 0 0 0Potassium-Reedmerg-0 0 0 0 0 0 0 0 0 0nerite Albite 0 0 0 9 0 0 0 0 0 0Sodium-Zinc-Silicate 25 27 28 28 30 28 25 27 18 25Cordierite 5 5 6 0 0 0 5 0 0 0Vlasovite 0 0 0 0 0 0 0 0 0 0Calcium-Zirconium-Sili-20 18 16 16 20 22 15 20 20 20cate Potassium-Niobium-Sili-0 0 0 0 0 0 5 5 12 5cate Silicon Dioxide 50 50 50 47 50 50 50 48 50 50Diboron Trioxide 0 0 0 0 0 0 0 0 0 0Calculated Properties CTE / (ppm / K) 4.65 4.86 4.98 5.30 5.09 4.87 4.72 4.91 4.02 4.63Removal rate ISO 695 / 46.7 48.5 50.3 51 46.6 44.8 51.1 47.5 46.0 46.4(mg / (dm²3h)) pH (50 µmol / l H2O) 8.92 8.93 8.94 8.93 8.94 8.93 8.91 8.94 8.87 8.91Removal rate DIN 12116 0.43 0.42 0.44 0.40 0.34 0.34 0.42 0.36 0.35 0.34Annealing point / °C 748 738 732 727 725 735 739 731 763 741Working point / °C 1319 1310 1306 1323 1292 1301 1303 1276 1308 1299The following embodiments have been melted and analyzed. In the following table, the meas-ured values are listed. The results show that measured values and calculated values are ingood agreement. Table 18 Example No. 27 40 41 48 62 70CTE / (ppm / K) 5.0 4.7 4.8 4.4 4.6 4.7Removal rate ISO 695 / 45 5 29 43 28 29(mg / (dm²3h)) ISO 719 Consumption0.08 0.03 0.04 0.02 0.04 0.050.01 M HCl pro g / (mL / g) Removal rate DIN 12116 0.4 0.3 0.3 0.5 0.5 0.5 / (mg / (dm²6h)) Annealing point / °C 604 702 692 736 677 680Working point / °C 1206 1286 1272 1293 1306 128215 December 2023 51 / 59

Claims

Claims1. Glass comprising the following components in the indicated proportions (in mol%):Component Min MaxSiO2 70 85ZrO2 0 5Nb2O5 0 8B2O3 0 9Al2O3 0 3ZnO 0 7MgO 0 3CaO 0 8Na2O 0 8K2O 0 8wherein the sum of the proportions of ZrO2 and Nb2O5 is at least 1.0 mol%, wherein thesum of the proportions of Na2O and K2O is at least 3.0 mol%, wherein the composition ofthe glass is characterized by the following constituent phases (in mol%): Constituent Phase Min MaxReedmergnerite 0 50Potassium-Reedmergnerite 0 25Albite 0 15Sodium-Zinc-Silicate 0 35Cordierite 0 15Vlasovite 0 30Calcium-Zirconium-Silicate 0 30Potassium-Niobium-Silicate 0 50Silicon Dioxide 15 60Diboron Trioxide 0 10wherein the sum of the proportions of vlasovite, calcium-zirconium-silicate and potassium-niobium-silicate is at least 5.0 mol%.

2. The glass according to claim 1, wherein the removal rate r according to ISO 695 calculatedaccording to following formula (2)is at most 75 mg / (dm23h), wherein c is a constant of dimension mg / (dm23h) having the nu-merical value 356.23, wherein M / MSiO2is calculated according to following formula (4)15 December 2023 52 / 59wherein MSiO2 is 60.084 g, wherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein Mi is the molar mass of the i-th constituent phase, wherein n is the number of constituent phases of the glass composition, wherein N / NSiO2 is calculated according to the following formula (5)wherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein zi is the number of atoms per building unit in the i-th constituent phase, wherein n is the number of constituent phases of the glass composition,wherein f is the number of 3D angle degrees of freedom per atom and f is calculated ac-cording to the following formula (3)wherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein zi is the number of atoms per building unit in the i-th constituent phase, wherein fi is the number of angle degrees of freedom per atom in the i-th constituent phase, wherein n isthe number of constituent phases of the glass composition, wherein c‘ is a dimensionlessconstant having the numerical value 0, wherein Λ is the optical basicity calculated accord-ing to the following formula (7)wherein ci is the molar proportion of the i-th constituent phase of the glass composition,wherein n is the number of constituent phases of the glass composition, and wherein thenumerical values of αi and βi are listed in the following table for the individual constituentphases: Constituent Phase αi βiReedmergnerite 1.741875 2Potassium-Reedmergnerite 1.71625 2Albite 1.761375 2Sodium-Zinc-Silicate 1.4472 1.6December 2023 53 / 59Constituent Phase αi βiCordierite 1.783777778 2Vlasovite 1.621166667 1.833333333Calcium-Zirconium-Silicate 1.520571429 1.714285714Potassium-Niobium-Silicate 2.002166667 2.333333333Silicon Dioxide 1.696 2Diboron Trioxide 2.355 3.

3. The glass according to at least one of the preceding claims, wherein the removal rate ac-cording to DIN 12116 calculated according to formula (19) ^= 0.0096is at most 0.7 mg / (dm26h), wherein ΔM1 is calculated according to the following formulawherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein n is the number of constituent phases of the glass composition, wherein the numer- ical values of μi are listed in the following table for each constituent phase: Constituent Phase μiReedmergnerite 9.05021Potassium-Reedmergnerite 9.30871Albite 23.441Sodium-Zinc-Silicate 24.0227Cordierite 40.4059Vlasovite 24.6482Calcium-Zirconium-Silicate 25.0007Potassium-Niobium-Silicate 24.4656Silicon Dioxide 0Diboron Trioxide 31.0824wherein ΔM2is calculated according to the following formula (14) ∆^ = ^^^^ ∙^ wherein M is calculated according to the following formula15 December 2023 54 / 59wherein ciis the molar proportion of the i-th constituent phase of the glass composition, wherein n is the number of constituent phases of the glass composition, wherein the numer- ical values of Miare listed in the following table for each constituent phase: Constituent Phase MiReedmergnerite 61.51275Potassium-Reedmergnerite 65.53975Albite 65.5555Sodium-Zinc-Silicate 64.722Cordierite 64.9944444Vlasovite 70.9228333Calcium-Zirconium-Silicate 67.9588571Potassium-Niobium-Silicate 100.05656Silicon Dioxide 60.084Diboron Trioxide 69.619wherein Z2is calculated according to the following formulawherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein n is the number of constituent phases of the glass composition, wherein the numer- ical values of ζi are listed in the following table for each constituent phase: Constituent Phase ζiReedmergnerite 0.501519Potassium-Reedmergnerite 0.450004Albite 1.24214Sodium-Zinc-Silicate 0.646597Cordierite 2.30471Vlasovite 0.798872Calcium-Zirconium-Silicate 0.841821Potassium-Niobium-Silicate 0.810568Silicon Dioxide 0Diboron Trioxide 2.67882wherein O is calculated according to the following formulaDecember 2023 55 / 59wherein ci is the molar proportion of the i-th constituent phase of the glass composition, wherein n is the number of constituent phases of the glass composition, wherein the numer- ical values of Oi are listed in the following table for each constituent phase: Constituent Phase OiReedmergnerite 2Potassium-Reedmergnerite 2Albite 2Sodium-Zinc-Silicate 1.6Cordierite 2Vlasovite 2Calcium-Zirconium-Silicate 1.71Potassium-Niobium-Silicate 2.33Silicon Dioxide 2Diboron Trioxide 3wherein ε is calculated according to the following formula (16)4. The glass according to at least one of the preceding claims, wherein the pH calculated bysolving system of equations (1) is less than 9.0.

5. The glass according to at least one of the preceding claims, wherein the average linear co-efficient of thermal expansion (CTE) in the temperature range 20°C - 300°C calculated ac-cording to following formula (21) 27,205^ ^^^ / ^is at most 6.0 ppm / K, wherein ^ ^^^^^^^^^ is calculated according to following formula (20)wherein m is the number of cation types present, Epot,j is the potential well depth of the j-thcation type and zj,iis the number of cations of the j-th type in the i-th constituent phase, wherein ci is the molar proportion of the i-th constituent phase of the glass composition andwherein n is the number of constituent phases of the glass composition.

6. The glass according to at least one of the preceding claims, wherein the working point cal-culated according to formula (29) is at most 1350 °C.15 December 2023 56 / 597. The glass according to at least one of the preceding claims, wherein the annealing pointcalculated according to formula (30) is in a range of from 600 to 875 °C.

8. The glass according to at least one of the preceding claims, comprising the following com-ponents in the indicated proportions (in mol%):Component Min MaxSiO2 75 85ZrO2 1 3Nb2O5 0 7B2O3 0 8Al2O3 0 2ZnO 0 6MgO 0 2CaO 1 6Na2O 0.5 6K2O 0 7wherein the sum of the proportions of ZrO2 and Nb2O5 is at least 1.0 mol%, wherein thesum of the proportions of Na2O and K2O is at least 4.0 mol%, wherein the composition ofthe glass is characterized by the following constituent phases (in mol%): Constituent Phase Min MaxReedmergnerite 0 40Potassium-Reedmergnerite 0 20Albite 0 5Sodium-Zinc-Silicate 0 30Cordierite 0 10Vlasovite 0 15Calcium-Zirconium-Silicate 1 25Potassium-Niobium-Silicate 0 45Silicon Dioxide 20 55Diboron Trioxide 0 5wherein the sum of the proportions of vlasovite, calcium-zirconium-silicate and potassium-niobium-silicate is at least 5.0 mol%.

9. The glass according to at least one of the preceding claims, wherein the removal rate r ac-cording to ISO 695 calculated according to formula (2) is at most 70 mg / (dm23h).

10. The glass according to at least one of the preceding claims, wherein the removal rate ac-cording to DIN 12116 calculated according to formulas (19) is at most 0.6 mg / (dm26h).15 December 2023 57 / 5911. The glass according to at least one of the preceding claims, wherein the pH calculated bysolving system of equations (1) as an estimate of the pH obtained by dissolving 50 µmol glass in one liter of neutral water is less than 8.95.

12. The glass according to at least one of the preceding claims, wherein the average linear co-efficient of thermal expansion (CTE) in the temperature range 20°C - 300°C calculated ac-cording to formula (21) is at most 5.0 ppm / K.

13. The glass according to at least one of the preceding claims, wherein the working point cal-culated according to formula (29) is at most 1340 °C.

14. The glass according to at least one of the preceding claims, wherein the annealing point cal-culated according to formula (30) is at most 825 °C.

15. The glass according to at least one of the preceding claims, wherein ^ ^^^^^^^^^ calculated ac-cording to following formula (20) is in a range of from 1500 kJ / mol to 1800 kJ / mol.

16. The glass according to at least one of the preceding claims, wherein the ratio of the sum ofthe proportions of Na2O and K2O to the sum of the proportions of ZrO2and Nb2O5is in a range of from 0.5 to 6.0.

17. Method for producing the glass of at least one of the preceding claims, the method compris-ing the following steps: a) Melting glass raw materials,b) Optionally forming a glass article, in particular a glass tube, from the melt,c) Cooling the glass.

18. Method according to claim 17, wherein forming comprises a drawing method, in particulartube drawing.

19. Use of the glass according to at least one of claims 1 to 16 as or for pharmaceutical pack-aging.15 December 2023 58 / 59

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