through a boundary conductance, h, on faces at z = +/- L.
is controlled by the parameter hL/k, the Biot Number, where k is the thermal conductivity of the material. A large Biot number implies that heat is applied faster than it can be absorbed in the plate; a small Biot number implies that the temperature is quickly transferred through the plate, giving small temperature gradients and low thermal stress.
The motivation for doing new thermal stress tests of very thin sapphire is that the thinness of the material should make its response to heating very different from that of the standard thickness of sapphire microwave windows. As the sapphire becomes thinner and thinner the time needed for a given temperature to propagate into the sapphire becomes less and less. Since the temperature propagates rapidly to the face opposite the heat input, large temperature gradients through the thickness do not exist for sufficiently thin windows. For typical windows, if there is a heat input to one face, this face heats and expands. The opposite, cooler face expands less and is in tension, compressing the hot face. The cold, relatively weak surface of the sapphire is thus where fracture occurs. For very thin sapphire windows this thermal stress buildup does not occur.
For initial experiments a 2 mm thick, irregularly shaped piece of sapphire was quenched in room temperature water and fracture resulted as the temperature was raised to temperatures similar to that reported above. A 0.5 mm thick piece of sapphire also fractured when quenched from 200°C, but the fracture propagated from the edge of the small piece, rather than throughout the area, as did the thicker sapphire. This implied that the damaging thermal gradient was over the width, not the thickness. Next, a soldering iron was used to create a hot spot in the sapphire. First, a standard pencil soldering iron was used to create spot heating to 200°C (measured), without fracturing this thickness of sapphire. Next, a high power soldering gun was used to raise the spot temperature to 500°C, still without fracturing the sapphire. This confirmed that the water quench was a much more severe test than simple spot heating. Spot cooling was performed by placing a drop of water on a heated piece of sapphire. A drop of water falling on the center of a 200°C piece of either the thick or thin sapphire did not fracture either piece. At 300°C a wet Q-tip did fracture the thicker piece, but not the thinner piece. The thinner piece could not be fractured at any temperature, because at higher temperatures the boiling water forms a vapor barrier to heat transfer at the surface that prevents large amounts of heat transfer.
Applying a heat source to a very thin piece of sapphire thus results in a uniform hot spot at one area in the sapphire plate surrounded by a dropping temperature around this area. The spot has expanded and is compressed by the cooler material around it. However, the tensile stress in the outer sapphire is distributed throughout the bulk of the material, and is spread around a much larger area than the spot being heated. Thus thermal stresses are much lower for a very thin sapphire window.
It is concluded that the thin windows developed in this program will be significantly more tolerant of high power microwaves than current power scaling predictions based on decreasing the thickness of the window.
The windows developed in this program can thus be considered to be true thermal membranes, in the sense that the windows are so thin that the temperature through the thickness of the window is constant. Thermal stress in these windows will be a result of expansion in the plane of the window. This will cause the disk to flex rather than create tension in the plane of the disk. Furthermore, the tensile stress will be distributed throughout the thickness of the disk and will be distributed around the periphery of the hot section. Both of these effects will reduce the levels of maximum stress. As a result, the disks should withstand much more heating than is currently possible. None of this would apply for arc heating, which is very localized and would result in large local thermal stresses. However, the resulting stresses in this case as well will be much reduced compared with thick disks.
Total Stress Design. The combination of thermal and mechanical stress determines the overall stress levels in the sapphire. In the case of a membrane the center of the window is in tension as a result of pressure stress, and in compression as a result of thermal stress. The window must be designed with a safety factor at its worst case point of operation, which in this case is where the window is cold. As the window heats up the compressive stress formed at the center will remove some of the pressure tension and increase the window safety factor during operation.
Vacuum Design. Sapphire is an excellent material for vacuum applications. It has no internal volatiles because strength requirements require a perfect single crystal. Surface adsorption is negligible as a result of the near perfect polish required for strengthening. High temperature active metal brazing is used in fabrication to permit high temperature bakeout, and these brazes have excellent vacuum properties. Weld attachment of the brazed window completes the high quality vacuum design of the fixture.
Material Design Strength. The factors that are involved in specifying single crystal sapphire are discussed in the background section. An important factor in microwave window design is the need for large pieces of sapphire. High power microwave systems require larger diameter waveguides and windows. Current 1 MW 110 GHz systems use 75 - 100 mm diameter windows. A best-quality piece of sapphire of this size is expensive in small quantities. With a careful window design, however, it is only necessary to have defect free sapphire in the regions of maximum stress - at the center of the disk; the outer part of the disk can possess some defects. Since sapphire is grown in boules that tend to be defect free at the center but with increasing numbers of defects at increasing radius, it may be acceptable and much cheaper to obtain material that has some defects around the outside diameter.
As a result of the axial symmetry of the microwave power deposition, sapphire is almost always used with its c-axis coincident with the window axis. If another orientation is used the asymmetry in the thermal properties of the window caused by similar asymmetries in the crystal will cause asymmetry in the thermal stress, unpredictable stresses and probably failure in marginal applications. This may not be the case for the thin windows of this program, since the thermal gradients are small.
To date sapphire has been the material of choice for microwave window applications because it has a high strength and a low loss tangent. As both microwave power and frequency (window absorption increases with frequency at room temperature) have increased, standard sapphire windows have reached their limits and are currently a major constraint on the development of high power microwave systems. For this reason other materials (or combinations of materials) have been developed.
At this time the leading window material is chemical vapor deposited (CVD) diamond. Silicon nitride has also been considered, since it has a loss tangent comparable with sapphire and is considered as a result of better thermal properties and perhaps higher strength. Diamond is normally much stronger than sapphire, and its very high thermal conductivity makes edge cooling practical (Table 3). Its low permittivity results in very low reflection.
Table 3. Thermal and loss tangent properties of microwave window material candidates.
Material................Thermal Conductivity(W/mK)....................Loss Tangent
........................................300K..........77K..............................300K..............77K
Silicon (AU-doped)........200...........2000........................20 x 10-6.......10 x 10-6
Sapphire............................60...........1000........................200 x 10-6.......5 x 10-6
Diamond(CVD).............2000...........6000.........................50 x 10-6.......50 x 10-6 (150K)
The strength and thermal conductivity of CVD diamond has made it the leading candidate to replace sapphire in microwave window applications. The ability to edge cool the windows is a major advantage of diamond, avoiding complex flow passages in the microwave channel and only requiring one window. For many applications, however, double windows will be required for safety reasons, where redundancy is required. The primary problems with diamond windows are price and quality. Although the best quality CVD diamond is true diamond the CVD process does tend to create "diamond-like carbon (DLC)" and graphite at the grain boundaries. If the CVD process is not fully optimized this non-diamond material can significantly increase the loss tangent and create a real quality control issue.
Very thin sapphire windows will have losses comparable with diamond at significantly lower cost. Another major advantage that sapphire has over CVD diamond is its resistance to radiation - diamond is an excellent radiation detector. Strengthened sapphire is as strong as CVD polycrystalline diamond (about 1.2 GPa tensile strength). CVD diamond cannot be polish strengthened because its strength is controlled by the weakness of its grain boundaries rather than flaws in its surface. Sapphire also has the potential for much lower microwave losses as a result of its large reduction in loss tangent at cryogenic temperatures, where it also becomes somewhat stronger. If polishing costs can be kept down, the biggest advantage sapphire windows will have over diamond will be cost.
This work consisted of the design, fabrication, and testing of the window fixture and its components. The goal of the task was to develop a prototype megawatt microwave window fixture and to test it under realistic conditions, except for the high power testing of Task 4. The primary technique used to increase the microwave transmission power capability compared with standard windows was to make a fixture with sapphire windows that are much thinner than those used in current practice, but supporting the same pressure loads. The thinner windows absorb a much lower fraction of the microwave power passing through them and thus permit much higher transmission before failure.
The windows were made thinner first by strengthening the sapphire, as discussed in Task 1, but also by reducing the maximum stress in the window for the same pressure and thus allowing a window with a fixed strength to survive a higher pressure. The two physical effects that were used to reduce the maximum tensile strength in the disk (the compressive strength of sapphire at room temperature is much higher) were cantilevering at the edge and membrane stress distribution as discussed and explored in Task 1. This task created fabrication techniques that were appropriate to a high vacuum, bakeable fixture to achieve and that would also lead to the desired stress reduction in the window.
Fixture Geometry Design. The basic design was to make a high temperature seal at or near the outer window diameter, and to provide a loading pivot at some lesser diameter. Possible additional constraints were 1) providing the capability to preload the outer diameter by adjusting its initial vertical deflection, and 2) providing the capability to fix the outer edge radially. Constraints that arise from non-mechanical issues include the fact that the fixture design must be compatible with double-disk cooling, that it be compatible with total transmission of microwave power, that it not cost too much, and that it be practical to fabricate. The final prototype geometry and design is discussed in Task 5, but the window brazing technique developed in this task allowed a redesigned assembly that simplified even the standard double window fixture and formed an elegant final prototype window fixture design.
Fixture Fabrication To fabricate a prototype window fixture, 76 mm diameter, 0.043 mm thick sapphire disks were used, together with old window fixtures available at ORNL from Dr. Bigelow's laboratory. These fixtures were built to form a double disk window for standard 63.5 mm inside diameter waveguide. They originally had alumina disks brazed on, but these disks had been cracked during earlier use.
Two brazing designs were defined and tested: the first was edge brazing of a window in a tube, and the second was flat brazing to a ring. The flat braze simulates a braze to a cup, similar to the standard window fixture. The purpose of these tests was to determine if the sapphire windows would survive the metalization and brazing process, and to determine the stress and deflection in the windows resulting from the brazing.
Preliminary analysis of the stresses in the brazed piece indicate that the moment, stress, and deflection generated in the sapphire disk is limited by the strength of the metal it is brazed to. Calculation of the stresses indicates that they can be very large, such that only very soft materials that yield at low stresses can be used in the joint to prevent breaking the sapphire. Normally the temperature of the braze would be an important factor in that it controls the total thermal expansion mismatch that must be accommodated in the joint. However, the thermal stresses that are caused are so great that the yield strength of the metal (or the break strength of the sapphire) is reached at even lower temperatures than that used for soldering. This would imply that the higher temperatures associated with brazing can be tolerated; this conclusion was tested in brazing experiments.
For these experiments three 76 mm diameter wafers were purchased. These wafers are the cheapest thin sapphire material available for testing, but they have the disadvantage of being R-plane disks and having the orientation flat cut out of the edge. The extensive (and proprietary) brazing work was performed by 3E Laboratories to develop the sapphire window fixture fabrications techniques. The brazing was done at high temperature (900°C) to demonstrate a joint that could be baked out at temperatures as high as 600°C.
Brazing into the end of a tube had the advantage that the external metal would be able to keep the braze joint and sapphire in compression as the part cooled from brazing temperature. The tube thickness, tube strength, and type of metal were chosen so that the metal would yield in response to the tensile stresses on it and limit the maximum stress in the joint. This braze joint was unsuccessful, breaking the window, but the failure was not one of the technique. The UC wafer windows all have an alignment flat on the edge for electronics processing; the window broke where the flat diverged from the tube wall. The differential stress at the corner of the gap between the wafer flat and the tube caused the break. Rather than try to match the tube end shape to the wafer shape or pay much more to get a round window, the face braze test was attempted next.
The face braze consisted of using a 89 mm OD and 63.5 mm ID very thin metal ring brazed to the outside of the 76 mm OD sapphire window. The metal ring was annealed to be as soft as possible to minimize thermal stresses during the brazing process. The initial braze attempt was successful, but left a gap between the window and the ring at a local azimuthal position as a result of bowing of the metal ring. Although past practice had shown that rebrazing causes failure of the window, a rebraze under a heavier weight was attempted because the part was useless as it was. The rebraze was successful without difficulty, illustrating the robustness of the design and demonstrating the feasibility of the process. A second assembly was then brazed in a similar manner for inclusion in the final window prototype.