Low helium permeability atomic frequency standard cell and method for forming same
BACKGROUND OF THE INVENTION 
     This invention relates to atomic frequency standard cells such as cesium and rubidium cells, and to methods for fabricating such cells. 
     Optically pumped atomic frequency standards using alkali metal such as cesium and rubidium vapor have come into wide spread use as basic frequency standards. Weidemann U.S. Pat. No. 4,661,782 provides a general introduction to such frequency standards. Generally speaking, a gas cell is provided within a resonant microwave cavity. In a rubidium gas cell frequency standard, for example, microwave resonance in the rubidium is detected by measuring the absorption of a suitable optical radiation which is directed at the gas cell while the resonant cavity is excited by externally generated microwave radiation. The frequency of this microwave radiation is controlled according to the degree of absorption of the optical radiation. 
     When permanent gases such as helium, hydrogen, and nitrogen are present inside a reference cell containing the rubidium atoms, these gases act to shift (increase or decrease) the atomic reference frequency. (A &#34;permanent gas&#34; is a substance that exists completely in the vapor phase at all temperatures and pressures of interest.) The amount of the shift depends on the type of gas and the density of the gas in the cell and is therefore proportional to the partial pressure of the gas in the cell. 
     At 100° C. and below, glass is essentially impermeable to most gases. Helium and hydrogen are two exceptions to this statement. Since the helium atom has greater permeability than the hydrogen molecule, glass is much more permeable to helium than to hydrogen, and, helium that is normally present in the atmosphere in small amounts can slowly permeate a glass cell. (Hydrogen is also present in the atmosphere, but at ten times lower concentration than helium). This results in a helium concentration inside the cell that changes with time. 
     If the cell initially has no helium inside, then helium from the atmosphere will slowly pass through the glass and the helium density inside the cell will increase with time. The density increases to a final steady-state value which is equal to the density of helium in the atmosphere. At this point the permeation of helium through the glass stops because there is no longer any pressure differential across the glass walls of the cell. Typically this process takes years to stabilize, and the permeation rate is largest at the start. 
     The accumulation of helium inside the cell produces a frequency shift in the output frequency of the standard that varies with time. This behavior contributes to the overall frequency aging of the standard. Such aging is highly undesirable, because one of the reasons for using a rubidium frequency standard is that it exhibits low aging compared to less expensive devices, such as stand-alone crystal oscillators. 
     The rate at which helium accumulates in a cell (atoms/cc/sec) depends on the total permeation rate (atoms/sec) and the volume. The permeation rate is proportional to the total surface area of the cell. Generally speaking, as a cell is made smaller, its volume to surface area ratio decreases; i.e., the volume fills up faster with helium in a smaller cell because there is proportionally more surface area available for permeation. Thus, as cells are made smaller, the need for glass with lower helium permeability becomes more important. 
     Various approaches have been proposed for containing alkali metal vapor in a suitable cell, as discussed in the following U.S. Patents: 
     
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U.S. Pat. No.       Inventor
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3,242,423           L. Malnar
3,248,666           D. J. Farmer
3,510,758           G. R. Huggett
3,577,069           L. Malnar
3,675,067           H. Brun
4,405,905           Busca et al.
4,494,085           S. Goldberg
4,569,962           H. Robinson
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     The cells described in the Malnar, Brun, Busca, and Huggett patents all rely on cells that are blown from a suitable glass. This approach brings with it a number of important disadvantages. First, skilled glass-blowers are needed to form such cells, and it is progressively more difficult to achieve uniform dimensions of the cells as they are made smaller. Furthermore, when gas cells are made smaller there is an increased importance in using low helium permeability glasses, and some low helium permeability glasses are difficult to work using glass-blowing techniques. 
     Another approach discussed in the Farmer patent is to eliminate the glass cell entirely and instead to supply windows in the metal walls of the microwave resonant cavity. The Farmer patent expressly recognizes the difficulty in manufacturing gas cells of glass or quartz to sufficiently close tolerances, and attempts to avoid these problems by eliminating the glass cell entirely. In the resonating cavity of Farmer, the windows 16, 17 are of glass, and they may be sealed to the resonator 10 by glass to metal seals using fusible rings attached to the cylindrical extensions 18, 20. The approach taken in the Farmer patent allows the alkali vapor gas to come into contact with the metal walls of the resonating cavity. Furthermore, it is not possible to replace the gas without simultaneously replacing the resonating cavity. 
     SUMMARY OF THE INVENTION 
     It is an object of this invention to provide a precisely dimensioned cell for an atomic frequency standard having low helium permeability, which can be manufactured without the use of specialized glass-blowing skills, which can be readily manufactured at a relatively low cost, and which can be filled with the desired gas in a conventional manner. 
     According to a first aspect of this invention, an atomic frequency standard cell is provided comprising a cell body defining first and second annular sealing surfaces. First and second windows are sealed to respective ones of the sealing surfaces to form a cell, and a fill tube communicates with an opening in the cell and is sealed thereto. The cell is shaped and configured as an atomic frequency standard cell, and the cell body and windows are formed of glasses having respective helium permeabilities less than about K(T)=1×10 -11  for T=100° C., where K(T) is helium permeability expressed in cubic centimeters of helium per second at 760 torr, 25° C. for 1 cm 2  of glass having a thickness of 1 mm when a helium partial pressure difference of 1 torr is applied across the glass. This cell preferably has a volume less than 60 cubic centimeters. 
     According to a second aspect of this invention, a method is provided for forming an atomic frequency standard cell having low helium permeability. First and second windows and a cell body are provided, the body defining first and second annular sealing surfaces, and one of the windows and the body defining an opening. The windows and the body are all formed of glasses having respective helium permeabilities less than K(T)=1×10 -11  for T equals 100° C. The first and second windows are sealed to the respective sealing surfaces of the body to form a cell having a volume no greater than 60 cubic centimeters. A tube is sealed to the cell adjacent to the opening to form a fill tube for the cell. 
     Preferably, the body, windows and tube comprise aluminosilicate glass, and annular fusible gaskets comprising borosilicate glasses are positioned between the windows and the respective annular sealing surfaces. The sealing step preferably comprises a step of heating the body and the windows to a temperature of no more than about 850° C. for a time sufficient to fuse the gaskets and seal the windows to the body. 
     The invention itself, together with further objects and attendant advantages, will best be understood by reference to the following detailed description taken in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an exploded perspective view of the components of an atomic frequency standard cell which incorporates a presently preferred embodiment of this invention, prior to fabrication. 
     FIG. 2 is a cross-sectional view of the cell of FIG. 1 at the completion of fabrication. 
     FIG. 3 is a perspective view of the cell of FIG. 2 at a first intermediate stage of fabrication. 
     FIG. 4 is a cross-sectional view taken along line 4--4 of FIG. 3. 
     FIG. 5 is a perspective view of selected components of the cell of FIG. 2 at a second intermediate stage in fabrication. 
     FIG. 6 is a side view in partial section of the cell of FIG. 2 at a third intermediate stage in fabrication. 
     FIG. 7 is a graph showing a preferred heating cycle used in the fabrication of the cell of FIG. 2. 
    
    
     DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS 
     Turning now to the drawings, FIGS. 1 and 2 show exploded perspective and cross sectional views of an atomic frequency standard cell 10 which incorporates a presently preferred embodiment of this invention. The cell 10 includes a cylindrical, tubular body 12 which defines spaced, parallel, annular sealing surfaces 14. The cell 10 also includes first and second windows 16, one of which defines a central opening 18. Annular, fusible window gaskets 20 are positioned between the sealing surfaces 14 and the windows 16, and a fill tube 22 is positioned in the opening 18. A fusible tubular gasket 24 is positioned around the fill tube 22 to seal the fill tube 22 to the adjacent window 16. 
     The various component elements of the cell 10 can readily be manufactured as discrete components. For example, the fill tube 22, the body 12 and the gaskets 20, 24 can be cut from glass tubes. The materials chosen for the elements of the cell 10 are carefully selected to have the desired thermal and helium permeability characteristics. In particular, the gaskets 20, 24 are formed of materials having a lower softening temperature than that of the body 12, the windows 16 and the tube 22 such that when the assembled cell 10 is heated to the proper temperature, the gaskets 20, 24 fuse to seal the windows 16 to the body 12 and the fill tube 22 to the window 16, and yet the body 12, the windows 16 and the tube 22 do not substantially alter their shape. 
     The preferred method for forming the cell 10 is illustrated in FIGS. 3-6. As shown in FIGS. 3 and 4, a first step in this method is to assemble the windows 16, window gaskets 20 and body 12 in a stack on a support element 30. The assembled components are placed within a jig 32, 34 which is loosely held together by fasteners 36. The support surface 30 is oriented horizontally such that the windows 16 are oriented horizontally. The jig 32, 34 can be pressed together to position the body 12, the windows 16 and the window gaskets 20 concentric with respect to one another. The jig 32, 34 is then moved out of contact with the assembled elements of the cell 10. The assembly shown in FIGS. 3 and 4 is then brought to a suitable temperature to cause the window gaskets 20 to fuse and thereby to seal the windows 16 to the body 12. The sealed assembly is then allowed to cool at a controlled rate to anneal the assembly. 
     The next step in the fabrication of the cell 10 is to place the tube gasket 24 on the fill tube 22 and to support the fill tube in a horizontal orientation, with the tube gasket 24 spaced from the end of the fill tube 22 by a small amount (1 mm in this example). Then the combination of the fill tube 22 and the assembled tube gasket 24 is heated as described above to cause the tube gasket 24 to fuse to form a bead like shape at one end of the fill tube 22. As shown in FIG. 5, a small length (approximately 1/2 mm in this embodiment) of the fill tube 22 protrudes beyond the fused tube gasket 24. 
     The third step in the preferred method for forming the cell 10 is to place the body 12 with the sealed windows 16 in place in a fixture 40 which includes a support surface 42. The fixture 40 supports two vertical supports 44 which are provided with adjustable flanges 46. Then the fill tube 22 is positioned with the end of the fill tube 22 in the opening 18 and the fused tube gasket 24 in contact with the adjacent window 16. The upper end of the fill tube 22 is positioned within a riser 48 that defines a head 50. The riser 48 is freely slidable in an opening in a beam 52 which rests on the flanges 46. The fixture 40 is adjusted such that the head 50 of the riser 48 protrudes approximately 1 mm above the beam 52. The weight of the riser 48 presses the fill tube 22 downwardly, thereby pressing the fused tube gasket 24 into contact with the window 16. This assembly is then heated as described above, thereby softening the tube gasket 24. Once the tube gasket 24 is softened, the weight of the riser 48 pushes the fill tube 24 downwardly by about 1 mm and thereby presses the fused tube gasket 24 into sealing contact with the adjacent window 16, to produce the finished cell 10 of FIG. 2. 
     As pointed out above, it is particularly important when constructing a small frequency standard cell of the type described above to maintain helium permeability of the walls of the cell at an adequately low level. 
     The total amount, q, of helium gas permeating a thin glass wall of area A and thickness d in a time t is given by 
     
         q(T,t)=K(T)·(A/d)·δp·t,   (1) 
    
     where K(T) is the helium permeation constant for the glass at temperature T, and δp is the pressure differential of helium across the wall. Using this formula, it can be shown that the instantaneous rate of pressure rise inside a closed volume, V, due to helium permeation through the walls, is 
     
         dp/dt=δp/τ,                                      (2) 
    
     where 
     
         τ=0.392·V·d/[K(T)·A·T].(3) 
    
     Here, p is in torr; K is the helium permeation constant which is the permeability in cc of helium per second at NTP (760 torr, 25° C.) for 1 cm 2  of glass having a thickness of 1 mm when a helium partial pressure difference of 1 torr is applied across the glass; A is the total surface area of glass in cm 2  ; V is in cc; d is in mm; and T is the cell temperature in degrees Kelvin. 
     The relationship between the shift δf in the output frequency of the standard due to helium in the cell and the partial pressure of helium inside the cell is given by 
     
         y=C.sub.1 ·p,                                     (4) 
    
     where 
     
         C.sub.1 ≈+0.80×10.sup.-7 /torr @ 100° C.(5) 
    
     and y=fractional frequency offset due to helium=δf/f. 
     Combining Eqs. (2) and (4), we obtain the frequency aging, 
     
         R(t)≡dy(t)/dt=[C.sub.1 ·δp.sub.o /τ]·e.sup.-1/τ                           (6) 
    
     where δp o  is the initial value of the helium partial pressure difference across the cell wall, which is positive if the helium pressure outside the cell is greater than that inside. 
     The result obtained in Eq. (6) shows that if the cell is placed in an environment where the helium partial pressure is constant, then the aging rate at t=O, R o , is given by 
     
         R.sub.o ≡R(O)=C.sub.1 ·δp.sub.o /τ,(7) 
    
     and the aging rate thereafter decreases exponentially with time constant τ. Typically, τ is a long time, on the order of years. For this reason the aging when the unit is new is of primary interest, which is also when the aging rate is greatest. In this case, t&lt;&lt;τ and dy/dt is approximately equal to the value at t=0, namely R o . 
     Combining Eq. (3), (5) and (7), we obtain 
     
         R.sub.o =2.04×10.sup.-7 ·[δp.sub.o ·K(T)·A·T]/(V·d).     (8) 
    
     If the cell contains no helium at the time of manufacture, and the frequency standard is operated at sea level in the earth&#39;s atmosphere, then δp=4.0×10 -3  torr and the above equation becomes 
     
         R.sub.o =8.16×10.sup.-10 ·[K(T)·A·T]/(V·d).    (9) 
    
     For a given acceptable aging rate, this equation can be used to set an upper limit on the permeation constant as a function of the surface-area-to-volume ratio and the glass thickness: 
     
         K(T)≦(1.23×10.sup.9 ·R.sub.o /T)·d/(A/V).(10) 
    
     As the cell gets smaller, the surface-area-to-volume ratio increases and it is clear from this equation that the largest acceptable value of the permeation constant decreases. 
     Small military rubidium frequency standards having a claimed aging performance of 1×10 -22  per month (3.8×10 -18  /sec) are presently available. Since there is more than one source of aging in a rubidium frequency standard (&#34;RFS&#34;), a good rule of thumb is, if possible, to limit each contributor to approximately one-tenth of the total desired aging. For this reason, R o  =3.8×10 -19  /sec is a reasonable value to use in the above equations. 
     To be competitive, a military RFS typically either uses a cell that operates at high temperature (≈100° C.), or else uses a thermoelectric cooler to maintain a lower cell temperature when higher ambient temperatures are encountered. The latter approach is more complicated and expensive, and therefore the former approach of a cell able to operate at high temperatures is desirable. For this reason, a cell operating temperature of 100° C. is assumed in the following analysis. 
     Using the above values of R o  and T, Eq. (10) becomes 
     
         K(T)≦1.25×10.sup.-12 ·d/(A/V).       (11) 
    
     As an example, we may take a cylindrical cell of circular cross section (inside dimensions of radius R and length L) for which A=2πR(R+L) and V=πR 2  L. In this case, 
     
         A/V=2(1/L+1/R), cylindrical cell.                          (12) 
    
     In the case of a small cylindrical cell with L=0.7 cm and R=0.55 cm, A/V=6.5 and from Eq. (11) we have that 
     
         K(T)≦1.9×10.sup.-13 ·d.              (13) 
    
     For most practical cells, d≈1 mm. In this case, 
     
         K(T)≦1.9×10.sup.-13, d=1 mm.                  (14) 
    
     Aluminosilicate glass such as Corning 1720 glass has a low enough helium permeation constant to satisfy the requirement of Eq. (14), and it satisfies the requirements by more than two orders of magnitude; since other aluminosilicate glasses are expected to have approximately the same helium permeation constant as Corning 1720, they are also expected to be suitable for use in small cells. 
     Similar considerations also apply for cells having other geometrical shapes. The general case can be treated using Eq. (11) which gives the maximum allowable value of the permeation constant as a function of (A/V) and d. Conversely, for a given glass and permeation constant, Eq. (11) can be used to determine the smallest allowable value of (A/V)/d. 
     Operation of an RFS in a helium-enriched and/or hydrogen-enriched atmosphere would impose an even more stringent condition on the maximum allowable value of permeation constant for a given value of (A/V). 
     For the reasons set out above, the preferred material for the body 12, the window 16 and the fill tube 22 is an aluminosilicate glass such as Corning 1720 or 1724. The preferred material for the gaskets 20, 24 is a borosilicate glass such as Corning 7052. Borosilicate glass has a lower softening point than does aluminosilicate glass, and thus is well suited for forming the sealing gaskets 20, 24. Additionally, the coefficients of thermal expansion of these two materials are closely matched. Aluminosilicate glass has a suitably low helium permeability constant K(T) (less than 2×10 -13  for T equals 100° C.). Borosilicate glass, though it has a higher helium permeability constant, makes up only a small fraction of the total area of the cell 10. 
     Table 1 provides presently preferred dimensions and materials for the components of the cell 10, which has a volume of about 0.66 cc. In Table 1 all dimensions are in inches, and the dimensions for the gaskets 20, 24 are taken after fabrication of the cell 10 has been completed. 
     
                       TABLE 1
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                 Wall
Element Height   Thickness  ID    OD    Material*
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body 12 .220     .040       --    .52   1
window 16
        .040     --         --    .52   1
fill tube 22
        2.0      --         .040   .080 1
window  .030     .040       --    .52   2
gasket 20
fill tube
        .060     --         .080  .19   2
gasket 24
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 *Material 1 is an aluminosilicate glass such as Corning 1724; Material 2
 is a borosilicate glass such as Corning 7052 or 7056.
 
    
     In order to minimize distortion of the window 16 adjacent the fill tube 22, the heating cycle is preferably conducted at a relatively low temperature of less than 850° C. and preferably about 845° C. for about one hour. FIG. 7 defines the preferred heating cycle used for the three sealing operations described above. As shown in FIG. 7, the cooling rate is preferably controlled to allow at least seven minutes in the anneal range for aluminosilicate glass (660°-750° C.) and at least seven minutes in the anneal range for borosilicate glass (430°-500° C.) Vibration is preferably minimized during the heating cycle, and a travelling belt furnace can be used The surfaces to be sealed should be clean and free of particle contamination. 
     The preferred material for the support surfaces 30, 42, the jig 32, 34, and the beam 52 is a refractory material such as that sold under the trade name Lava by Minnesota Mining &amp; Manufacturing. The remaining components of the fixture 40 can be formed of stainless steel. Of course, all of these details of construction are provided merely to define the best mode presently contemplated by the inventor, and these details are not intended to limit the scope of this invention. 
     After the cell has been fabricated as discussed above, it can be filled in the conventional manner with a gas comprising an alkali metal vapor such as cesium or rubidium vapor. The fill tube 22 can then be sealed in the conventional manner to close the cell 10. 
     The cell 10 and the method for forming the cell 10 described above provide a number of important advantages. First, all of the component parts can be manufactured separately in automatic or semi-automatic operations. The cell itself can be manufactured in a low cost, repeatable manner without the use of specialized glass-blowing skills Because the body of the cell functions as a spacer which defines the separation between the windows and therefore the optical path length of the cell, the separation between the windows can be precisely controlled at a desired value simply by properly dimensioning the component parts. The fill tube allows the cell to be filled in the conventional manner without glass blowing skills, and the sealed cell provides low helium permeability and is well suited for a small volume cell. The windows are flat and free of thermal deformation, and much of the window that receives the fill tube is itself unobstructed. This invention is particularly useful in small volume cells having a volume less than 60 cc, and preferably less than 10 cc. 
     Of course, it should be understood that a wide range of changes and modifications can be made to the preferred embodiments described above. Alternate materials can be substituted for the particular glasses disclosed above, and the cell 10 can be shaped as desired. For example, cross-sectional shapes other than the circular shape shown can readily be obtained. If desired, the fill tube can be mounted in an opening in the body as opposed to one of the windows, and the fill tube may not protrude into the opening. Also, pressed sintered parts made from glass powder and a suitable binder may be used. 
     It is therefore intended that the foregoing detailed description be regarded illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, which are intended to define the scope of this invention.