Abstract:
A glass for sealing a beta-alumina tube in a sodium-sulphur cell has a composition suitable to resist attack by sodium at elevated temperatures and a coefficient of thermal expansion suitable for use with beta-alumina. The glass consists essentially of 28-48 mol % B 2  O 3 , 0-20 mol % SiO 2 , 16-28 mol % Al 2  O 3 , together with 18-33 mol % of at least one alkaline earth oxide selected from the group consisting of BaO, SrO, CaO and MgO, the proportions of the constituents being such that the combined total of B 2  O 3  and SiO 2  is 40 to 60 mol % and furthermore being such that 0.0517 A 1  +0.0354 A 2  -0.0063 A 3  +0.168 A 4  +0.1336 A 5  +0.098 A 6  +0.1597 A 7 , lies between 5.7 and 6.4 where A 1 , A 2 , A 3 , A 4 , A 5 , A 6  and A 7  are the respective molar percentages of B 2  O 3 , SiO 2 , Al 2  O 3 , BaO, CaO, MgO and SrO. 
     A cell sealed with such a glass is described.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to glass seals for beta-alumina in electro-chemical cells and other energy conversion devices containing sodium and to glasses for use in such seals. 
     2. Prior Art 
     In cells, such as for example sodium-sulphur cells, and other devices (e.g. sodium-sodium thermo-electric generators) where beta-alumina ceramic is used as a solid electrolyte through which sodium ions can pass, it is necessary to seal the beta-alumina in the cell structure. Sodium sulphur cells utilise a molten alkali metal and have to operate at elevated temperatures where the electrode materials are liquid. Seals necessary to seal these electrode materials within the cells have therefore not only to withstand highly reactive materials at these elevated temperatures but are also subjected to temperature cycling. As a typical example, a sodium sulphur cell might contain a beta-alumina electrolyte tube closed at one end and having sodium on one face of the tube, preferably the outer face, and the sulphur/polysulphides on the other face. The cell has to be sealed to prevent escape or mixing of these materials and a number of proposals have been made for the sealing of such cells. Compared with most metals, ceramic materials are generally weak, particularly in tensile strength and it is necessary therefore in any seal for such a cell to ensure that the ceramic material is not overstressed. 
     It is well-known in a sodium sulphur cell to provide a beta-alumina electrolyte tube with an alpha-alumina tubular extension at its open end so that the end portion is ionically insulative. The alpha-alumina and beta-alumina have similar coefficients of thermal expansion and the alpha-alumina extension can be secured to the beta-alumina with a glass seal. 
     The present invention is concerned more particularly with such glass seals. The use of glass seals is described, for example in U.S. Pat. Nos. 3,928,071, 3,826,685 and 3,868,273. These references however do not discuss the glass composition. It is convenient, in sodium sulphur cells and similar electro-chemical cells to use a glass as a bonding agent between ceramic materials or between a ceramic material and a metal member. In a sodium sulphur cell, the closure may be effected by sealing the ceramic electrolyte material to a closure member or to the housing. This may readily be done with a glass seal. The alpha-alumina extension then has to be sealed to the housing or to the closure member. The closure member may be a part of a current collector. Thus glass may be employed, in sealing a cell, as a bond between solid electrolyte material, e.g. beta-alumina ceramic, or an insulating ceramic, e.g. alpha-alumina, and a metal component or components such as a current collector, an intermediate component, or an external housing. The glass-to-metal bond is formed by a reaction between the glass and an oxide layer on the metal. 
     Both for sealing alumina to metal and for sealing beta-alumina to alpha-alumina, the glass employed must be a sodium-resistant glass. The metal material has to be chosen in accordance with both mechanical and chemical requirements. In particular, it must resist attack by sodium at elevated temperatures. It is the practice in sodium sulphur cells to use mild steel or stainless steel for the housing, in contact with the sodium. 
     In particular, use has heretofore been made of a glass, commonly known as BAB glass. As is described in U.S. Pat. No. 3,275,358, this glass, which has a composition by weight of about 40% B 2  O 3 , 25% Al 2  O 3  and 35% BaO can be used for providing a fused hermetic seal around lead wires of tantalum and other similar metals. Expressed in molar percentages, the composition of this glass is about 54.8% B 2  O 3 , 23.4% Al 2  O 3  and 21.8% BaO. 
     This BAB glass however does not fully meet the difficult service conditions of seals for sodium-sulphur cells, particularly alpha to beta alumina seals, which place a severe demand on the performance of the sealing glass used. The required characteristics of such a glass in terms of its physical and chemical properties are many and sometimes conflicting and so the development of a glass composition approaching the desired behaviour is of necessity a complex process. It must produce a reliable hermetic seal and hence must wet both the alpha and beta alumina. The glass should be chemically compatible with cell materials at cell operating temperatures. The thermal expansion characteristics of the glass and the other seal components must be compatible to give low seal stresses over the whole working temperature range and lifetime of the cell. 
     In general, most stable glasses will satisfactorily wet both alpha and beta alumina and so could potentially satisfy the first criterion. The requirement as the chemical compatability considerably constrains the choice of glasses to the use of the alumino-borate glasses because of their known good sodium resistance. The requirements about thermal expansion characteristics are not satisfactorily met by BAB Glass. 
     It is necessary to consider in further detail the problems of seal stresses. The theory and practice of glassed seals, notably glass-to-metal seals, is very well established: See, for example, &#34;Glass-to-Metal Seals&#34; by J. H. Partridge, Soc. for Glass Technology, Sheffield 1949 and &#34;Glass-to-metal Seals&#34; by A. W. Hull and E. E. Burger, Physics 5. 384-405 1934. One of the most important factors contributing to successful seal performance is the close thermal matching of the seal components. Differential thermal strain causes seal stresses which, if sufficiently high, can result in seal failure. 
     At high temperatures when a seal is made, the glass is fluid and wets the ceramic components. On cooling, the viscosity of the glass rapidly increases and eventually it becomes so high that the glass behaves as a rigid material. It is convenient for analysis to idealise the transition between the fluid and rigid regions as occurring suddenly at a single temperature called the set point, even though in reality the change takes place over a small range of temperatures. Above the set point any thermal stresses developed in the glass are relieved by viscous flow. However, at the set point the glass becomes rigid and mechanically constrains the seal components, so that on further cooling, stresses are developed due to the subsequent differences in thermal strain characteristics. 
     A convenient graphical construction to assess the magnitude of the differential strain is shown in FIG. 1 of the accompanying drawings where the expansion/contraction characteristics (dimension change plotted as ordinate against temperature as abscissa) of the seal components are plotted and the characteristics are vertically displaced so as to intersect the set point. Assuming that the seal components are elastic, the stresses generated at any temperature are proportional to the vertical separations of the two curves in FIG. 1, and so the stress-temperature characteristic has the shape shown in FIG. 2, in which the stress is plotted as ordinate against temperature as abscissa. 
     For sodium-sulphur cells, the properties of the ceramics to be joined are effectively fixed. The main seal stresses in the glass are material dependent only and are not greatly influenced by seal geometry except at points close to the seal edges. The composition of the sealing glass does however have an important effect on the seal stress characteristics. 
     Because of its brittle nature, glass has a much higher strength in compression than in tension. Thus, for good seal strength, a high crossover temperature (see FIGS. 1 and 2) is desirable so that the seal stresses are compressive both at room temperature and operating temperature (typically 300°-400° C.). This is not the only criterion for satisfactory seal stresses because seal cracking and failure can also occur if the room temperature stress is too highly compressive. 
     All glasses have non-linear thermal strain characteristics and these are such that a sealing glass will always be in tension at high temperatures. By using a glass with a high set point, it is possible to have both a high crossover temperature and a moderate room temperature compressive stress as is shown in FIG. 3, which is a diagram similar to FIG. 2 but for two further different glasses. 
     Seals made with BAB glass have a generally tensile seal stress characteristic and tend to crack easily in thermal cycling of sodium sulphur cells. An additional disadvantage of this glass is a high densification rate. Densification, sometimes called stabilisation, is a process of molecular reordering of a glass at temperatures below the glass transition point, resulting in a gradual shrinkage of the material. When constrained within the seal components, the sealing glass is thereby subjected to increasing tensile stresses, which can cause seal failure if they grow sufficiently large. It might appear that improvement could be obtained by altering the relative proportions of the three constituents in this glass. However, as will be apparent from consideration of the data given by C. Hiramaya, J. Amer. Ceram. Soc. 1961, 44(12), 602-6 on this ternary system that the particular composition or BAB glass is on the edge of the glass forming region of the phase diagram of this three-phase system and it has not been found possible to satisfactorily lower the expansion coefficient of the glass of this ternary system by altering the proportions of the components. 
     SUMMARY OF THE INVENTION 
     According to the present invention, a glass for sealing to beta-alumina in an electro-chemical cell or other energy conversion device containing sodium, consists essentially of: 
     (a) 40-60 mol % glass former consisting of 28-48 mol % B 2  O 3  and 0-20 mol % SiO 2   
     (b) 16-28 mol % Al 2  O 3   
     (c) 18-33 mol % of at least one alkaline earth oxide selected from the group consisting of BaO, CaO, MgO and SrO, 
     where the proportions of the constituents furthermore are such that: 
     
         0.0517A.sub.1 +0.0354A.sub.2 -0.0063A.sub.3 +0.168A.sub.4 +0.1336A.sub.5 +0.098A.sub.6 +0.1597A.sub.7 
    
     lies between 5.7 and 6.4, where A 1 , A 2 , A 3 , A 4 , A 5 , A 6  and A 7  are the respective molar percentages of B 2  O 3 , SiO 2 , Al 2  O 3 , BaO, CaO, MgO and SrO. 
     The coefficients of A 1 , A 2  etc. quoted above are, as will be explained later, truncated values of regression coefficients relating to effect of the constituent proportions on the mean linear coefficient of thermal expansion. 
     The proportion of Al 2  O 3  would usually be between 17 and 28 mol %. 
     The glass may contain one or more of the alkaline earth oxides; preferably the proportions of these oxides lie in the ranges 0-25 mol % BaO, 0-15 mol % SrO, 0-30 mol % CaO and 0-20 mol % MgO with a minimum total of 18 and a maximum total of 33 mol %. 
     It will be appreciated by those skilled in the art that some of the compositions defined above lie close to the boundary of the glass-forming region. These boundaries, such as those discussed with reference to alkali alumina borate glass systems by Hiramaya in the above-mentioned reference, are diffuse. Care has to be taken in the use of compositions in the boundary region because of the possibility of devitrification. 
     The invention furthermore includes within its scope a hermetic seal between ana lpha-alumina components and a beta-alumina component in a sodium sulphur cell comprising a glass body fused between surfaces of these components, the glass consisting essentially of 28-48 mol % B 2  O 3 , 0-20 mol % SiO 2 , 16-28 mol % Al 2  O 3 , together with 18-33 mol % of at least one alkaline earth oxide selected from the group consisting of BaO, SrO, CaO and MgO, the proportions of the constituents being such that the combined total of B 2  O 3  and SiO 2  is 40 to 60 mol % and furthermore being such that 0.0517 A 1  +0.0354 A 2  -0.0063 A 3  +0.168 A 4  +0.1336 A 5  +0.098 A 6  +0.1597 A 7 , lies between 5.7 and 6.4 where A 1 , A 2 , A 3 , A 4 , A 5 , A 6  and A 7  are the respective molar percentages of B 2  O 3 , SiO 2 , Al 2  O 3 , BaO, CaO, MgO and SrO. 
     The glass composition described above may employ silica to reduce the thermal expansion coefficient compared with that of a pure BAB glass and to improve its glass forming properties. 
     Additions of other alkaline earth oxides CaO, MgO and SrO within the prescribed range result in a glass having suitable seal stresses for operations in sodium/sulphur glassed seals and superior densification properties compared with a three component BAB glass. 
     For the range of compositions described above, various glass properties can be expressed as a linear algebraic summation of the kind. ##EQU1## where a is the property in question. 
     A i  is the linear coefficient for compound i. 
     a i  is the molar percentage of the compound i. 
     Implied in this relationship is the assumption that the contribution of each component to the overall glass behaviour is linear and independent of the amount and kind of other components present. This is unlikely to be generally true but, from experimental results this assumption appears to be acceptable over the composition range of interest. 
     The expression 0.0517 A 1  +0.0354 A 2  -0.0063A 3  +0.168A 4  +0.1336A 5  +0.098A 6  +0.1597A 7  when multiplied by 10 -6  gives the value of the mean linear coefficient of expansion between 25° and 500° C. (α 25   500 ) and thus the above-defined glass would have a coefficient between 5.7 and 6.4×10 -6  /°C. Using this expression, the possible glass compositions for any required coefficient of expansion can be determined and it is thus possible to determine the composition in accordance with a specific physical requirement, e.g. to match a measured coefficient of expansion of the beta-alumina. 
     A number of physical properties of glass compositions as defined above may be expressed in a similar way as a series of coefficients representing the molar effects of the various constituents which can be summed in a similar way to obtain the magnitude of a required parameter. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
     FIGS. 1, 2 and 3 are graphical diagrams referred to above, for explaining real stresses due to differing temperature characteristics of materials; 
     FIG. 4 is a trilinear coordinate composition diagram for glasses showing the molar proportions of glass-forming oxides comprising B 2  O 3  and SiO 2  (marked GO), Al 2  O 3  and alkaline earth oxides (marked RO); 
     FIG. 5 shows a number of examples plotted on an enlarged part of the diagram of FIG. 4; 
     FIGS. 6 and 7 illustrate respectively the forming of two different seals between an alpha-alumina and a beta-alumina component; and 
     FIG. 8 illustrates diagrammatically a sodium sulphur cell embodying the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A number of glass compositions within the present invention are set out in Table 1. This tables also includes, for comparison purposes, a BAB glass constituting example 597. For convenience, the thirtyone glasses in the table have been given, in the left-hand column, the Case Nos. 1-31. Example 597 is Case No. 1. 
     FIGS. 4 and 5 are trilinear co-ordinate composition diagrams. The shaded area in FIG. 4 indicates the general range of sealing glass compositions which are within the scope of this invention as set out in claim 1. The further part of the definition in terms of the coefficients A 1  to A 7  in claim 1 may further restrict the range of compositions according to the mixture of glass forming oxides GO and alkali oxides RO which is used. 
     The glasses of the present invention include, as explained above, B 2  O 3  and SiO 2  which are referred to as the glass-forming oxides (GO in FIGS. 4 and 5). In the glass compositions of the present invention, the higher the total of boron oxide and silicon oxide, the better are the glass-forming properties. However, the resistance to sodium attack is decreased. Increasing the boron to silicon ratio gives better sodium resistance, better wetting properties and lower firing temperature but decreases the working range and gives a higher densification rate. 
     Increase of Al 2  O 3  results in a lower expansion coefficient but reduces the glass-forming properties. It also raises the crossover temperature and glass transition temperature. 
     The preferred sodium oxide content is as low as possible, within the confines of the impurities of the raw materials used. Enhanced densification results from the inclusion of Na 2  O. The effect of deliberate addition of sodium oxide is shown in Table 3. Example 32 in that table is a glass having a composition, in molar percentages, of 46.63 B 2  O 3 , 6.75 SiO 2 . 20.51 Al 2  O 3 , 10.26 BaO, 6.52 CaO, 6.53 MgO and 2.8 Na 2  O. Example 33 has the composition 46.73 B 2  O 3 , 6.54 SiO 2 , 20.56 Al 2  O 3 , 7.48 BaO, 6.55 CaO, 6.54 SrO and 5.61 Na 2  O. 
     It will be seen that the problems of high expansion, high densification rate and reactivity to molten sodium which occur with BAB glass can be overcome by modifications of the glass compositions in the various ways described. 
     Table 1 below gives experimental and calculated data for thirtyone different glasses, identified by case numbers in the left-hand column, of which properties have been measured. All of these glasses, except Case 1 (Example 597), which is included for comparison purposes, lie within the scope defined above. 
     As has been stated above, a number of physical properties of glass compositions may be expressed, like the coefficient of thermal expansion, as a series of coefficients representing the molar effects of the various constituents, which can be summed to obtain the magnitude of the required parameter. Tables 2(a), 2(b), 2(c), 2(d), 2(e) and 2(f) set forth coefficients and compare observed and predicted values for the expansion coefficient, transformation temperature, deformation temperature, room temperature, seal stress, crossover temperature and change in seal stress due to densification respectively for the 31 glasses listed in Table 1. In each of Tables 2(a), 2(b), 2(c), 2(d), 2(e) and 2(f) Case No. 1 is the BAB glass which is outside the scope of the present invention and which is included for comparison purposes only. 
     It will be understood that, although the shaded area of FIG. 4 shows the composition ranges within which the glasses of the present invention lie, it does not constitute a definition of suitable glasses. The actual composition has to be chosen, as previously described, to obtain the required properties, e.g. expansion coefficient. As previously explained some of the compositions lie close to the boundary of the glass-forming region and care has to be taken, in the use of compositions in the boundary region, because of the possibility of devitrification. 
     It will be noted from Table 1 that the densification rates of all the glasses listed (except the BAB glass No. 597 which is included for comparison purposes) are below, and most are substantially below that of BAB glass. 
     For sealing alpha-alumina to beta-alumina, the above-described glass can be used in known ways, e.g. by the use of a glass powder or a glass preform. A very convenient way of sealing a cylindrical alpha-alumina element to an end of a beta-alumina tube is to introduce a ring of glass between these surfaces, the glass is then being fused to seal the alumina elements together. Such an arrangement is illustrated in FIG. 6 where there is shown the upper end of a beta-alumina electrolyte tube, which forms a separator between molten sodium and molten sulphur/polysulphides in a sodium sulphur cell. The end surface of the electrolyte tube 10 is sealed by glass 11 to a shoulder 12 formed in an alpha-alumina ring 13. FIG. 7 is another example of a seal; in this case the lower end of a beta-alumina electrolyte tube 20 is sealed by glass 21 to a shoulder 22 formed in an alpha-alumina closure plate 23. In each of these examples, the glass is fused and forms a hermetic seal between the beta-alumina and alpha-alumina components. 
     From Table 1 it will be seen that all the glasses tested have a transformation temperature Tg which is such that the sealing operation can be carried out at a relatively low temperature. The magnitude of the difference between the values of Tg and Td is indicative of the rate of change of viscosity with temperature and hence of the working range of the glass, which lies at a higher temperature between Td and the temperature at which the viscosity is 10 3  pascal seconds. All the glasses listed in Table 1 have a long working range, making them easy to form. The working range, for example, in every case is adequate for rod drawing. 
     In Table 2(a), the regression coefficients showing the effect on the expansion coefficient of variations in the amounts of the various components are set forth at the bottom of the table. These enable the expansion coefficient of a glass (within the range of possible compositions) to be calculated from the molar percentage composition. The above-mentioned expression 0.0517A 1  +0.0354A 2  -0.0063A 3  +0.168A 4  +0.1336A 5  +0.098A 6  +0.1597A 7  is equal to the expansion coefficient multiplied by 10 6 . It will be seen that the various coefficients in this expression are the regression coefficients of Table 2(a). 
     Using Table 2(b) in a similar way, the transformation temperature can be calculated from the regression coefficients; the transformation temperature is 5.26A 1  +6.30A 2  +7.27A 3  +4.93A 4  +6.97A 5  +7.27A 6  +5.87A 7 . Similarly from Table 2(c) the calculated deformation temperature is 5.45A 1  +6.92A 2  +7.62A 3  +5.58A 4  +7.18A 5  +7.71A 6  +5.87A 7 . 
     Table 1 shows the transformation and deformation temperatures calculated in this way and also the observed values. 
     Table 2(d) shows the room temperature seal stress. Using the regression coefficients of this table, a room temperature seal stress of less than a predetermined value, e.g. 50 N/mm 2  can be ensured by using a composition in which 0.38A 1  +1.47A 2  +4.25A 3  -5.41A 4  -2.98A 5  -0.78A 6  -4.30A 7  is less than the predetermined value, e.g. 50 N/mm 2 . It will be noted that, in all the examples in Table 1, the room temperature seal stress is compressive. 
     Table 2(e) shows the cross-over temperature and the regression coefficients whereby this may be calculated. If the cross-over temperature is to exceed a predetermined value, e.g. 240° C., then the composition is chosen so that 1.27A 1  +9.24A 2  +31.26A 3  -28.39A 4  -15.01A 5  -2.54A 6  -23.29A 7  is in excess of said predetermined value. 
     Table 2f shows the change in seal stress due to densification at 400° C. for the first 100 hours. This stress change subsequently slows down, but may continue to increase even after a long period. For all the examples in Table 1, the change in seal stress due to densification is either to increase a tensile seal stress or decrease a compressive seal stress at 400° C. Using Table 2(f), the stress change due to densification at 400° C. for the first 100 hours, can be calculated from the regression coefficients; the stress change due to densification is 0.322A 1  +0.0016A 2  -0.218A 3  +0.139A 4  -0.190A 5  -0.238A 6  -0.036A 7 . In applications of this invention, the densification rate should be kept as low as practicable in keeping with the other requirement described in this specification. 
     FIG. 8 is a diagrammatic representation of a sodium-sulphur cell. In this particular cell, a cylindrical housing 30, typically a metal housing, surrounds a beta-alumina tube 31 which separates a first annular region 32, between the housing 30 and outer surface of the tube 31, from a second annular region 33 between the inner surface of the tube 31 and a co-axial current collector 34. One of these regions is the anodic region and the other is the cathodic region. In this particular example, the cell is of the central sulphur type, and has sulphur/polysulphides forming the cathodic reactant in the region 33 and has sodium in the region 32. The beta-alumina tube 31 is open at the top end and, around this end of the tube, is an alpha-alumina collar 35. A first closure 36 extends between the collar 35 and housing 30 to seal the annular region 32 whilst a second collar 37 extends between the collar 35 and current collector 34 to seal the region 33. 
     The collar 35 is sealed to the beta-alumina tube 31 by a glass seal using a glass as has been described above. The techniques described above enable a suitable glass to be chosen which will not unduly stress the beta-alumina tube. The same glass may also be used for other seals in the cell, if glass seals are employed. The closure members 36, 37 would usually be metal and may be welded to the housing 30, if the latter is of metal and also welded to the current collector 34 if that is metal. The seal between the closure member and the alpha-alumina collar may use glass or may employ diffusion bonding. 
     
                                           TABLE 1__________________________________________________________________________                        Trans-                              De-                        formation                              formationmol %                        Temp (°C.)                              Temp (°C.)Case   Glass                     Tg    TdNo.   No. B.sub.2 O.sub.3     SiO.sub.2        Al.sub.2 O.sub.3            BaO               CaO                  MgO                     SrO                        Obs                           Calc                              Obs                                 Calc__________________________________________________________________________1  597 54.83     0  23.38            21.78               0  0  0  571                           566                              606                                 5982  644 47.46     7.85        23.13            21.55               0  0  0  576                           572                              611                                 6083  667 40.26     15.54        22.89            21.32               0  0  0  578                           581                              613                                 6204  668 42.82     15.26        22.48            19.44               0  0  0  577                           581                              613                                 6195  671 47.71     7.37        23.27            15.48               6.17                  0  0  588                           586                              618                                 6196  676 46.52     6.96        20.46            13.03               6.51                  6.51                     0  591                           594                              626                                 6277  681 37.12     7.20        25.97            14.85               7.42                  7.42                     0  612                           608                              649                                 6438  688 42.08     6.48        21.50            7.48               14.96                  7.49                     0  610                           614                              642                                 6459  689 42.13     6.39        21.52            7.48               7.48                  14.98                     0  622                           616                              653                                 64910 690 41.94     6.80        21.43            12.11               5.59                  12.13                     0  604                           605                              639                                 64011 692 42.10     6.48        21.51            0  7.48                  7.48                     14.97                        607                           613                              632                                 63712 698 45.0     14.25        21.23            13.52               6.01                  0  0  588                           589                              624                                 62413 706 44.0     13.74        20.70            10.79               10.78                  0  0  591                           547                              628                                 63014 720 34.4     14.09        24.06            13.76               6.82                  6.87                     0  613                           610                              647                                 64715 722 37.08     7.32        25.93            16.69               3.71                  9.26                     0  593                           605                              630                                 64116 723 37.34     6.98        26.12            11.20               14.63                  3.72                     0  615                           614                              650                                 64717 725 37.22     6.95        26.04            9.30               13.03                  3.73                     3.72                        607                           615                              637                                 64518 726 37.23     6.95        26.04            7.44               11.17                  3.73                     7.44                        623                           614                              645                                 64319 730 41.10     10.0        25.0            10.76               2.39                  2.39                     8.37                        601                           597                              635                                 62820 733 42.9     10.0        21.3            7.73               3.87                  7.73                     6.45                        600                           602                              630                                 63921 734 28.1     20.0        21.9            9.0               4.5                  9.0                     7.5                        624                           618                              664                                 65422 735 44.9     10.0        17.0            4.22               5.61                  14.05                     4.22                        609                           609                              642                                 64023 736 42.8     10.0        20.7            10.6               1.33                  10.6                     3.98                        598                           600                              633                                 63424 737 46.2     10.0        19.4            0  24.4                  0  0  621                           617                              650                                 64425 738 30.4     20.0        16.9            4.91               6.54                  16.35                     4.91                        623                           626                              657                                 66226 740 28.0     20.0        21.2            12.32               1.54                  12.32                     4.62                        619                           616                              662                                 65427 741 32.0     20.0        19.7            0  28.3                  0  0  634                           635                              664                                 66628 743 37.65     15 17.00            4.57               6.08                  15.20                     4.57                        618                           619                              646                                 65129 745 35.4     15 20.95            11.46               1.44                  11.46                     4.30                        609                           608                              647                                 64430 747 32.0     20 18.7            0  29.3                  0  0  637                           634                              668                                 66531 750 44.90     10 17.00            10.96               0  17.36                     0  608                           603                              642                                 638__________________________________________________________________________                            Densification      Expansion              Room Temp                     Crossover                            Rate      Coefficient              Seal Stress                     Temperature                            N/mm.sup.2 /100 Hrs   Case      (25.sup.500) × 10.sup. -6              N/mm.sup.2                     °C.                            @ 400° C.   No.      Obs Calc              Obs                 Calc                     Obs                        Calc                            Obs Calc__________________________________________________________________________   1  6.5 6.36              4.2                  2.3                     132                        182 15.8                                15.6   2  6.1 6.21              12.9                 11.1                     263                        243 --  13.2   3  6.01          6.08              21.9                 20.0                     345                        304 10.0                                10.9   4  5.91          5.89              27.1                 29.0                     343                        345 12.6                                11.6   5  5.83          6.02              22.8                 25.7                     323                        323 --  11.3   6  6.26          6.23              19.4                 19.9                     298                        278 9.6 9.6   7  6.23          6.24              25.0                 26.8                     384                        373 3.8 5.2   8  6.28          6.27              23.0                 26.0                     320                        324 5.7 5.3   9  6.04          6.01              39.8                 42.4                     387                        422 4.4 4.9   10 6.25          6.26              21.5                 25.4                     307                        327 6.9 6.6   11 6.40          6.40              20.0                 24.4                     305                        305 5.1 5.2   12 5.89          5.78              28.8                 37.2                     350                        378 --  10.6   13 5.93          5.89              32.6                 34.4                     365                        361 8.8 9.1   14 6.04          6.04              36.5                 35.9                     412                        415 5.2 4.8   15 6.27          6.24              27.9                 26.5                     386                        372 6.6 5.7   16 6.25          6.22              28.7                 28.3                     388                        380 4.4 4.2   17 6.22          6.28              27.6                 26.9                     385                        369 4.3 4.1   18 6.29          6.31              26.5                 26.5                     380                        365 4.1 4.1   19 6.11          6.03              35.4                 33.3                     390                        383 --  8.0   20 6.16          6.05              34.4                 34.3                     360                        364 --  7.5   21 6.11          6.23              31.2                 31.7                     -- 384 --  2.3   22 6.03          6.09              35.0                 35.3                     370                        342 9.0 6.8   23 6.01          6.08              43.8                 32.2                     360                        353 --  7.8   24 5.79          5.88              49.9                 42.0                     394                        391 --  6.0   25 6.24          6.27              31.0                 32.9                     374                        358 --  1.5   26 6.29          6.26              32.4                 29.4                     -- 371 --  2.7   27 6.00          6.02              42.5                 41.0                     430                        416 --  0.7   28 6.17          6.18              34.39                 34.3                     -- 351 --  4.1   29 6.31          6.17              30.83                 30.8                     -- 362 --  5.3   30 6.29          6.16              32.38                 33.8                     -- 369 --  0.7   31 6.13          6.13              31.89                 31.2                     -- 325 --  8.2__________________________________________________________________________ Note:- Room Temperature Seal Stress is compressive and densification stress change is tensile. 
    
     
                       TABLE 2(a)______________________________________ EXPN. COEFF      EXPN. COEFF (×  10.sup.-6)            (× 10.sup.-6)   % DE-CASE  OBSERVED   PREDICTED             VIA-NO.   VALUE      VALUE        RESIDUAL TION______________________________________1     6.5000     6.3636       0.13638  2.142     6.1000     6.2075       -0.10754 -1.733     6.0100     6.0851       -0.75077E-01                                  -1.234     5.9100     5.8938       0.16214E-01                                  0.285     5.8300     6.0195       -0.18946 -3.156     6.2600     6.2346       0.25382E-01                                  0.417     6.2300     6.2404       -0.10369E-01                                  0.178     6.2800     6.2714       0.85928E-02                                  0.149     6.0400     6.0115       0.28462E-01                                  0.4710    6.2500     6.2612       -0.11203E-01                                  -0.1811    6.4000     6.4004       -0.38403E-03                                  -0.0112    5.8900     5.7838       0.10623  1.8413    5.9300     5.8945       0.35542E-01                                  0.6014    6.0400     6.0368       0.32265E-02                                  0.0515    6.2700     6.2375       0.32455E-01                                  0.5216    6.2500     6.2224       0.27599E-01                                  0.4417    6.2200     6.2813       -0.61272E-01                                  -0.9818    6.2900     6.3119       -0.21869E-01                                  -0.3519    6.1100     6.0299       0.80135E-01                                  1.3320    6.1600     6.0558       0.10424  1.7221    6.1100     6.2286       -0.11859 -1.9022    6.0300     6.0927       -0.62698E-01                                  -1.0323    6.0100     6.0846       -0.74605E-01                                  -1.2324    5.7900     5.8849       -0.94874E-01                                  -1.6125    6.2400     6.2732       -0.33152E-01                                  -0.5326    6.2900     6.2594       0.30637E-01                                  0.4927    6.0000     6.0234       -0.23440E-01                                  -0.3928    6.1700     6.1842       -0.14247E-01                                  -0.2329    6.3100     6.1727       0.13735  2.2330    6.2900     6.1635       0.12650  2.0531    6.1300     6.1304       -0.43482E-03                                  -0.01STANDARD ERROR OF THE ESTIMATE =                      8.65618E-02______________________________________INDEPENDENT          REGRESSIONVARIABLE             COEFFICIENT______________________________________A         B.sub.2 O.sub.3                    A1    0.51788E-01B         SiO.sub.2      A2    0.354561E-01C         Al.sub.2 O.sub.3                    A3    -0.638905E-02D         BaO            A4    0.168660E         CaO            A5    0.133673F         MgO            A6    0.985400E-01G         SrO            A7    0.159706______________________________________ 
    
     
                       TABLE 2(b)______________________________________ TRANSFOR-   TRANSFOR- MATION      MATION TEMPER-     TEMPER- ATURE (°C.)             ATURE (°C.)CASE  OBSERVED    PREDICTED   RESID- % DEVI-NO.   VALUE       VALUE       UAL    ATION______________________________________1     571         565.60      5.2966 0.952     576         571.82      4.1788 0.733     578         581.10      -3.0983                                0.534     577         580.60      -3.5953                                -0.625     588         585.88      2.1192 0.366     591         594.14      -3.1412                                -0.537     612         608.31      3.6946 0.618     610         614.10      -4.0987                                -0.679     622         616.25      5.7536 0.9310    604         605.99      -1.9914                                -0.3311    607         612.90      -5.8974                                -0.9612    588         589.34      -1.3359                                -0.2313    591         596.82      -5.8225                                -0.9814    612         609.93      2.0700 0.3415    593         605.05      -12.051                                -1.9916    615         613.94      1.0624 0.1717    607         614.52      -7.5178                                -1.2218    623         614.20      8.8027 1.4319    601         597.05      3.9463 0.6620    600         602.66      -2.6614                                -0.4421    624         618.18      5.8161 0.9422    609         609.53      -0.53344                                -0.0923    598         600.45      -2.4490                                -0.4124    621         617.17      3.8344 0.6225    623         626.20      -3.2015                                -0.5126    619         615.52      3.4798 0.5727    634         634.94      -0.94428                                -0.1528    618         618.29      - 0.28501                                -0.0529    609         608.02      0.98053                                0.1630    637         634.65      2.3521 0.3731    608         602.86      5.1412 0.85STANDARD ERROR OF THE ESTIMATE =                      5.1633______________________________________INDEPENDENT         REGRESSIONVARIABLE            COEFFICIENT______________________________________A          B.sub.2 O.sub.3                   A1      5.25703B          SiO.sub.2    A2      6.30455C          Al.sub.2 O.sub.3                   A3      7.27117D          BaO          A4      4.92931E          CaO          A5      6.97477F          MgO          A6      7.26598G          SrO          A7      5.86500______________________________________ 
    
     
                       TABLE 2(c)______________________________________ DEFOR-      DEFOR- MATION      MATION TEMPER-     TEMPER- ATURE       ATURE (°C.)             (°C.)        % DE-CASE  OBSERVED    PREDICTED   RESID-  VIA-NO.   VALUE       VALUE       UAL     TION______________________________________1     606         598.54      7.4556  1.252     611         607.83      3.1727  0.523     613         620.22      -7.2244 -1.164     613         618.70      -5.6986 -0.925     618         619.11      -1.1145 -0.186     626         627.29      -1.2857 -0.207     649         643.43      5.5745  0.878     642         645.04      -3.0447 -0.479     653         648.92      4.0775  0.6310    639         640.18      -1.1778 -0.1811    632         637.45      -5.4513 -0.8612    624         624.24      -0.24004                                 -0.0413    628         630.26      -2.2612 -0.3614    647         647.00      0.17929E-02                                 0.0015    630         641.45      -11.452 -1.7916    650         646.46      3.5426  0.5517    637         645.47      -8.4734 -1.3118    645         643.56      1.4403  0.2219    635         628.41      6.5866  1.0520    630         633.82      -3.8239 -0.6021    664         654.27      9.7274  1.4922    642         640.49      1.5106  0.2423    633         633.97      -0.97308                                 -0.1524    650         644.15      5.8468  0.9125    657         662.05      -5.0536 -0.7626    662         654.35      7.6502  1.1727    664         666.18      -2.1789 -0.3328    646         651.71      -5.7095 -0.8829    647         644.20      2.8026  0.4430    668         665.74      2.2552  0.3431    642         638.47      3.5295  0.55STANDARD ERROR OF THE ESTIMATE =                      5.7767______________________________________INDEPENDENT         REGRESSIONVARIABLE            COEFFICIENT______________________________________A          B.sub.2 O.sub.3                   A1      5.45372B          SiO.sub.2    A2      6.91713C          Al.sub.2 O.sub.3                   A3      7.61673D          BaO          A4      5.57566E          CaO          A5      7.18260F          MgO          A6      7.70930G          SrO          S7      5.86502______________________________________ 
    
     
                       TABLE 2(d)______________________________________ ROOM TEMP   ROOM TEMP SEAL STRESS SEAL STRESS (N/mm.sup.2)             (N/mm.sup.2)         % DE-CASE  OBSERVED    PREDICTED            VIA-NO.   VALUE       VALUE       RESIDUAL TION______________________________________1     4.2000      2.3084      1.8916   81.942     12.900      11.107      1.7931   16.143     21.900      20.002      1.8976   9.494     27.100      29.006      -1.9059  -6.575     22.800      25.714      -2.9142  -11.336     19.400      19.910      -0.50976 -2.567     25.000      26.810      -1.8097  -6.758     23.000      26.077      -3.0767  -11.809     39.800      42.406      -2.6055  -6.1410    21.500      25.409      -3.9095  -15.3911    20.000      24.402      -4.4017  -18.0412    28.800      37.201      -8.4008  -22.5813    32.600      34.399      -1.7993  -5.2314    36.500      35.908      0.59161  1.6515    27.900      26.464      1.4359   5.4316    28.700      28.250      0.44985  1.5917    27.600      26.917      0.68296  2.5418    26.500      26.558      -0.58458E-01                                  -0.2219    35.400      33.294      2.1056   6.3220    34.400      34.328      0.72313E-01                                  0.2121    31.200      31.739      -0.53902 -1.7022    35.010      35.382      -0.37236 -1.0523    43.800      32.239      11.561   35.8624    49.970      42.088      7.8817   18.7325    31.050      32.901      -1.8511  -5.6326    32.400      29.395      3.0050   10.2227    42.500      41.041      1.4590   3.5528    34.390      34.306      0.84491E-01                                  0.2529    30.830      30.802      0.27737E-01                                  0.0930    32.380      33.817      -1.4370  -4.2531    31.890      31.233      0.65735  2.10STANDARD ERROR OF THE ESTIMATE =                       3.9348______________________________________INDEPENDENT         REGRESSIONVARIABLE            COEFFICIENT______________________________________A          B.sub.2 O.sub.3                   A1    0.381181B          SiO.sub.3    A2    1.46994C          Al.sub.2 O.sub.3                   A3    4.24762D          BaO          A4    -5.41328E          CaO          A5    -2.97645F          MgO          A6    -0.775451G          SrO          A7    -4.30683______________________________________ 
    
     
                       TABLE 2(e)______________________________________ CROSSOVER   CROSSOVER TEMPER-     TEMPER- ATURE (°C.)             ATURE (°C.)CASE  OBSERVED    PREDICTED   RESID- % DEVI-NO.   VALUE       VALUE       UAL    ATION______________________________________1     132         181.94      -49.942                                -27.452     263         243.43      19.566 8.043     345         304.73      40.273 13.224     343         345.97      -2.9699                                -0.865     323         323.89      -0.88649                                -0.276     298         278.62      19.379 6.967     384         373.45      10.553 2.838     320         329.39      -9.3863                                -2.859     387         422.03      -35.026                                -8.3010    307         327.33      -20.330                                -6.2111    305         305.65      -0.64716                                -0.2112    350         378.20      -28.201                                -7.4613    365         361.56      3.4433 0.9514    412         415.32      -3.3204                                -0.8015    386         372.07      13.931 3.7416    388         380.35      7.6496 2.0117    385         369.26      15.738 4.2618    380         363.65      16.354 4.5019    390         383.51      6.4855 1.6920    360         364.84      -4.8424                                -1.3321    350         384.29      -34.290                                -8.9222    370         342.60      27.399 8.0023    360         353.17      6.8289 1.9324    394         391.06      2.9408 0.7525    374         358.13      15.870 4.4326    350         371.12      -21.122                                -5.6927    430         416.23      13.772 3.3128    350         351.67      -1.6700                                -0.4729    350         362.07      -12.071                                -3.3330    350         369.96      -19.959                                -5.3931    350         325.50      24.496 7.53STANDARD ERROR OF THE ESTIMATE =                       22.723______________________________________INDEPENDENT        REGRESSIONVARIABLE           COEFFICIENT______________________________________A          B.sub.2 O.sub.3                  A1     1.26972B          SiO.sub.2   A2     9.23752C          Al.sub.2 O.sub.3                  A3     31.2554D          BaO         A4     -28.3943E          CaO         A5     -15.0136F          MgO         A6     -2.53581G          SrO         A7     -23.2933______________________________________ 
    
     
                       TABLE 2(f)______________________________________Densification Rates(N/mm.sup.2 at 400° C. in first 100 hours)Case No.    Observed Value                    Predicted Value______________________________________1           15.8         15.592           --           13.153           10           10.964           12.6         11.615           --           11.286           9.6          9.567           3.8          5.198           5.7          5.299           4.4          4.9410          6.9          6.5811          5.1          5.1412          --           10.6213          8.8          9.1314          5.2          4.8415          6.6          5.7116          4.4          4.2317          4.3          4.1118          4.1          4.0819          --           7.9720          --           7.4521          --           2.2922          9.0          6.7923          --           7.8424          --           6.0325          --           1.5226          --           2.7527          --           0.6628          --           4.1429          --           5.2930          --           0.6931          --           8.16______________________________________Independent          RegressionVariable             Coefficient______________________________________A          B.sub.2 O.sub.3                    A1    0.322B          SiO.sub.2     A2    0.0016C          Al.sub.2 O.sub.3                    A3    -0.218D          BaO           A4    0.139E          CaO           A5    -0.190F          MgO           A6    -0.238G          SrO           A7    -0.036______________________________________ 
    
     
                                           TABLE 3__________________________________________________________________________    Trans-    formation            Deformation                    Expansion                            Room Temp                                     Crossover                                             Densification    Temp (°C.)            Temp (°C.)                    Coefficient                            Seal Stress                                     Temperature                                             RateCase     Tg      Td      (25.sup.500) × 10.sup.-6                            N/mm.sup.2                                     °C.                                             N/mm.sup.2 /100 hrs @                                             400° C.No.   Glass No    Obs Calc            Obs Calc                    Obs Calc                            Obs  Calc                                     Obs Calc                                             Obs   Calc__________________________________________________________________________32 693   566 564 603 599 6.32                        6.60                            5.6  2.0 146 166 14.5  14.533 694   547 537 580 574 6.67                        5.93                            -16.9                                 -14.9                                     None                                         None                                             20.9  20__________________________________________________________________________ The negative values of the room temperature seal stress indicate tension instead of compression