Leaded glass windows have endured for hundreds of years. Lead is resistant to environmental degradation because of its protective oxide and toxicity to bacteria and plant life. Windows made of glass framed with lead and soldered with lead alloys have outlasted any made using wood framing. But, lead alloys have little structural strength, are as "heavy as lead" and prone to a phenomenon known as creep that causes them to slowly yield to the force of gravity. In order to keep large leaded glass windows from buckling, iron members are soldered to the lead for reinforcement. But, soldering to thick sections is difficult because the thick section acts as a heat sink. Consequently the iron supports used on traditional stained glass windows have been insubstantial. In order to separate a window into several lights (each containing several leaded panes) wood muntins have been used. These are prone to decay. In synagogues and churches of the 19th and early 20th centuries, leaded glass lights have often been inserted into iron frames with putty in order to allow them to swing open. The Chagall windows in Jerusalem use steel framing to support the lights. The "Epstein Window", which provided the inspiration for the Beth El process, also uses heavy iron or steel to separate the lights. In this window, the lights are artfully soldered to directly to the steel. The Epstein window probably dates from the late 19th century when its drapery glass was popular. This is corroborated by the extreme decay of the wood that originally surrounded it. The Epstein window proved that leaded glass lights could be soldered into heavy ironwork. How it was originally made is unknown. However, the process being described was able to restore it.
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In order to understand why soldering to heavy iron or steel is so difficult, we need to examine how heat flows by conduction.
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In the figure above, a soldering iron is drawn along a seam. At the tip of the soldering iron is a molten zone, at  , indicated by the solid oval. Surrounding the molten region are concentric isotherms. Looking in the direction of the motion of the soldering iron, indicated by the arrow, we can identify an isotherm along which the temperature is essentially the same as the ambient,  , e.g. the dotted oval. Ahead of the moving soldering iron we have a process region bounded by that isotherm. It is into this region that most of the heat flows. Since this isotherm stays inside the workpiece, the size of the workpiece is to all intents infinite. Were we to simply touch the soldering iron to the workpiece and wait until a molten zone of the size above were formed, the thermal geometry would be similar. Of course a molten zone may never form.
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Heat conduction is governed by the heat conduction partial differential equation. In spherical polar coordinates it is,
 (1)
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where  is temperature, 
is the thermal diffusivity and the remaining variables refer to the standard coordinates. Consider a case similar to that described above in which the soldering iron moves at a steady rate so that the temperature field ahead of it is steady in the moving coordinate system. Directly ahead of the moving iron, the temperature field will vary only with r.
This direction will be where the heat flux density is greatest. We can use this geometry to set an upper bound on the total heat flux by assuming that the workpiece is effectively infinite. Since equation (1) reduces to an ordinary differential equation, it is easily solved.
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A more practical approximation to the geometry of the figure above is obtained using cylindrical coordinates. In this case we are soldering along the edge of the bar in that figure. Our molten zone is imagined to be a vertical cylinder. The height of this cylinder is the thickness of the bar. The radius of the cylinder is half the width of the molten zone. In cylindrical coordinates the heat conduction equation is,
 (2)
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where the coordinates are those of the standard cylindrical system. On inspection, we can see that the last term is zero. Applying the same assumptions used for equation (1) we can find a solution equation (2). It turns out that the solutions for both equations (1) and (2) are very similar. Both solutions can be written,
 (3)
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where 
is the heat flux (e.g. watts) for either an entire spherical or cylindrical region, K is the heat conductivity (not the diffusivity),
is a characteristic dimension that is the radius of the molten zone in spherical coordinates or the thickness of the material in cylindrical coordinates, 
is the radius of the molten zone and
is the radius of the heat affected zone outside of which the temperature is ambient. The function in the denominator takes different forms for the two coordinate systems, but the numerical values are similar. In practice
is approximately double .
Making much larger than that implies a very slow job of soldering. As the heat affected zone gets larger, convection and radiation become important. Practically, it is very difficult to make
much larger than three times . In this way, convection and radiation limit whether any soldering is possible at all. For
equal to twice
, the value of f() is about 0.5 for a spherical system and 0.69 for a cylindrical system. When using equation (3), one should divide the flux by two since the actual system is either roughly hemispherical or roughly a half cylinder. Equation (3) somewhat overestimates the required flux but otherwise gives very good predictions of the heat flux needed for successfully soldering to steel bars.
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The most important term in equation (3) is the difference between the ambient temperature and the melting point. If the ambient temperature is room temperature equation (3) predicts impracticably large fluxes. Increasing
is the solution to successful soldering. Soldering has to be done in some form of furnace. Much commercial soldering is done in a furnace and no soldering iron or similar tool is required. There are several reasons why this in not a good approach for windows. First, the difference between the melting point of the lead cames and that of the solder is small. Combining this with the relatively large size of windows shows that the allowable gradient of temperature deviation is impracticably small. One can solder a microcircuit in a furnace and maintain a melting hierarchy with only lead-base solders. Soldering a window this way is much more difficult because the temperature gradients act over longer distances. Second, temperature gradients induce warpage. The larger
, the larger the gradients may become and consequently the greater the probability of breaking the window during processing. Third, windows are often so large that the entire window will not fit into a furnace. The Beth El process minimizes
consistent with keeping required heat fluxes tractable.
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As shown in the above figure, the window is fixtured in contact with a heat reservoir and enclosed in a furnace that covers the reservoir. Soldering is performed through an adjustable port in the top of the furnace.
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