The effort of this work was devoted to fabricating ultrathin strengthened sapphire disks and to accurately model the stresses in the disks. The work can be divided up into three parts: 1) polishing development, 2) stress modeling, and 3) window pressure testing. The design clear aperture diameter for the Phase 2 program is 90 mm. This is the appropriate size for the apparatus used for high power testing at ORNL.
Sapphire Fabrication. There were two sources of sapphire for the project: Meller Optics (Providence, RI) and Union Carbide (UC - Crystal Products Division, Washougal, WA). The bulk sapphire for the Meller windows was supplied by Crystal Systems (Salem, MA), whereas UC grows their own sapphire. Bulk sapphire is grown in boules using the controlled heat exchange technique.
A wide variety of sapphire samples were fabricated for the program. Aside from polishing samples, over 50 sapphire windows were included in the test program, varying in diameter from 12.5 mm to 102 mm, and in thickness from 0.33 mm to 2.0 mm. Window fabrication techniques varied as well. The worst surface finish used was the standard 80/50 optical polish, whereas the pieces with the best polish had a nearly epitaxial surface. Bulk material was usually the best quality, defect free sapphire, characterized by Crystal Systems as HEMEX, but some HEMLIGHT, samples were included as exceptions (where noted). Samples were primarily R-plane, with a few C-plane samples included for comparison and result verification. A full list of samples is given in Appendix A.
Polishing Development. A proprietary polishing process has been specified by Dr. Bates. The polishing process itself is highly proprietary, but some of the variables involved can be discussed. The polishing process takes place between two machine-driven, counterrotating surfaces. The sapphire disks are firmly but temporarily mounted on one surface; the other surface, known as a lap, provides the abrasive surface for the polishing process. The type of lap used, the rotation speed, the pressure, the grading of the diamond grits for each polishing step, the time for each step, and finally the parameters of the chemical polishing colloidal silica solution (acidity, concentration, temperature, refresh rate, etc.) are all important parameters for the overall process. There are also other practical issues associated with fabricating very thin disks: the possibility of breakage during handling, and the tendency of material to warp during machining, and the difficulty of removing polishing debris.
Figure 1. Illustration of stages of polish in the strengthening process.
Figure 1 shows the generic progression in polish that occurs during the polishing stages that are necessary to achieve polish strengthening. The standard 80/50 Scratch/Dig optical polish is shown on the left. The scratches that are shown are caused by polishing with diamond grit. For sapphire, the next level of polish beyond this type of standard optical surface is a nominal 5/10 polish that is termed epi because the finish is so close to an epitaxial surface. These surfaces are usually characterized by a surface roughness that is on the order of nanometers. For the purposes of strengthening, however, isolated flaws that are not a factor for overall roughness are responsible for the crack initiation that greatly reduces macroscopic strength. These must be removed totally to achieve a strengthened piece.
Figure 2. Illustration of subsurface damage in a piece with an epitaxial surface.
Even the removal of all surface scratches is not a sufficient condition for reliable strengthening. Subsurface damage must also be removed. Figure 2 shows schematically a cross section of a surface that has an epitaxial surface but subsurface damage. Subsurface damage is usually created by anomalous and extreme damage during rough polishing or cutting that is usually only detectable using acid etch procedures. In this program SEM inspection is used to perform non-destructive examination of sub-surface damage. It is believed that final chemical polishing masks subsurface damage by dissolving and redepositing sapphire so that some surface defects are actually filled in or covered over, but not removed. This phenomena is unimportant for optical purposes, but is again critical for strengthening.
At the end of the Phase 1 program there were apparently two commercial sources (Meller Optics, and Union Carbide) of polish strengthened sapphire, neither of which were aware that the sapphire that they were providing was sometimes strengthened. Strengthening is masked by (and is often responsible for) the normal statistical variation in the strength of sapphire. The amount of strengthening is ultimately determined by failure pressure, but SEM inspection has been used to demonstrate an adequate degree of polishing for strengthening.
A number of supposedly epitaxial disks were purchased from Union Carbide while polishing development took place as a joint effort between TvU and Meller Optics. The Union Carbide disks provided windows for the bulk of the testing of the program, as well as for the final prototype window fixture. SEM inspection indicated that the wafers had few enough defects that they should be polish strengthened, but the disks were not perfect epitaxial surface as advertised (and used in the electronics industry). Failure testing of these disks indicated that most, but not all, of the disks were strengthened. Union Carbide only makes a few sizes of disks, and only one side of the wafers is in some sense guaranteed to be epitaxial; the other side has a best effort polish. This means the wafers are mounted with the epi side on the low pressure side for maximum effectiveness.
At the beginning of the Phase 2 program, Meller Optics prepared of a set of 2.5 cm diameter thin disks to test polish strengthening using polishing procedures that were apparently identical to those that had been used in Phase 1. Failure testing of these disks showed no statistical evidence of strengthening. SEM inspection was then performed, showing that the disks had significant numbers of surface flaws, and were thus not truly epitaxial surfaces. Two problems were discovered, one fundamental and one a technical detail. The fundamental change in sapphire processing parameters compared with that of Phase 1 was that much thinner windows were polished. The thinner disks were required both for failure testing and for eventual use as microwave windows, but the change in thickness forced changes in the polishing processes using the same equipment. The fundamental problem was that the material was so thin that polishing debris could not be carried away from the between the polishing plates that were now very close together. This debris degrades the edge polish and sometimes the central polish. This was not the case for the thicker disks polished in Phase 1.
This problem was solved in the short term at Meller by beginning with larger (32 mm OD) disks, then cutting off the outer edges after polishing. At the same time, thicker 5 cm diameter disks from stock were repolished specifically to demonstrate strengthening. Two of the 5 cm disks were failure tested, and shown to be unstrengthened. SEM inspection of all of the newly polished disks again showed an inadequate polish. The problem was discovered when Meller examined their polishing process. They found that their supplier of polishing pads had changed the formulation without telling them.
At this point it became necessary to perform some detailed polishing research. Since Meller was working more than full time on production they could not pursue this research. They were able to donate two old and cannibalized polishing machines to TvU for refurbishment and use to achieve the program and Phase 3 goals. The manuals for these Strasbaugh machines were obtained from the manufacturer. The gearing and bearings from the machines were removed for cleaning and bearing replacement where needed, the necessary replacement parts were ordered and installed, and the machines returned to working order.
Extensive polishing tests were performed and discussed with Meller. Much of the success of polishing is an art rather than a science. Experiments indicated that multiple polishing attempts with diamond grit were inherently unsuccessful; the polishing had to be set up and run in one attempt. Furthermore, material removal using chemical polishing was not done at Meller, only superficial polishing, a process that inherently cannot remove subsurface damage. Higher material removal rate chemical polishing is being pursued at TvU, iterating with SEM inspection to develop a final polish strengthening process. Although some strengthened samples have been obtained (enough to provide strengthened windows), a reliable polish strengthening process had not been developed at this writing. This work will be continued in Phase 3; TvU still believes that it can develop an appropriate polishing technique.
Stress Modeling. For preparation of the Phase 1 proposal and during the Phase 1 program experimental testing showed that the failure pressures observed during hydrostatic testing of thin sapphire windows were well above that predicted by the standard theory of bending disks.
The standard and accepted analysis of the stress for microwave window disks is that of a uniformly distributed load on a thin disk [13]. The loading diagram is shown in Fig. 3 for a disk function of radius a, thickness h, and the load q. The maximum stress σmax at the center of the disk is then
σ max = 3(3 + ν)qa2/8h2
where ν is Poisson's ratio. For sapphire, ν = 0.25, and the equation can be rewritten as:
σmax = 1.22qa2/h2
Figure 3. Loading diagram for an edge mounted thin disk.
Initial failure testing indicated that the window loadings observed were too high to be explained by either the standard strength of sapphire (tensile strength = 420 MPa) or even the strengthened sapphire (by a factor of 3 - 4) if the standard theory was used and R was taken to be the radius of the aperture for hydraulic tests as is normally the case. There was no question that either some other stress-reducing mechanism was taking place or that the above modeling for the maximum stress in the disk did not apply in some respect. The flexing thin disk model is well established and has been tested for accuracy for use with standard sapphire microwave windows in the past.
This contradiction between actual and predicted failure loading was resolved during Phase 2 work. The detailed modeling and the comparison with results will be discussed below. Before this is done the physical effects that are occurring which make the standard flexing thin disk theory inappropriate will be discussed.
The primary changes to the standard disk modeling that will be described here are the different boundary conditions at the edge of the disk and the addition of membrane effects. The flexing disk model discussed above assumes that the edges of the disk can move freely both radially and in edge surface angle. It also assumes that the center deflection of the disk is small - less than half the thickness of the disk. For the thin sapphire windows of this program both of these assumptions are not correct, and a more complete theory must be used.
The major change required in the simply supported disk model for the relatively early thick disk tests is that of the edge boundary condition. The first hydraulic tests of 1 mm thick 2.5 cm diameter disks performed in an earlier NASA program [14] used O-rings to seal the window. These O-rings were necessarily placed at a larger diameter than the window aperture, so that the O-ring would be contained and function properly. As a result, the actual loading diagram of the window was thought to be as shown in Fig. 4, for an aperture radius a1 and a sealing radius a.
Figure 4. Loading diagram for an edge mounted thin disk.
The window was assumed to be in contact with the surface at the O-ring. For larger radii the net loading on the window disappears as a result of equal pressures on both sides of the window. The complete load diagram indicates that the disk has a significant bending moment imposed at the aperture as a result of the loading at a larger radius than the aperture.
This was interpreted as a cantilevering effect. The loading outside the aperture will counterbalance the pressure inside the aperture (transmitted moment) and lead to an overall stress reduction at the center of disk where the stress is at a maximum. This reduces the maximum stress on the disk for the same pressure if the radius of the disk is increased beyond the radius of the aperture.
Using a simple area balance of the loading inside and outside the aperture radius, a new effective loading area was derived for calculating the maximum stress at the center of the disc. If the outer radius of the pressure loading is q and the radius of the aperture is ai, then the fractional decrease in effective loading area would be approximately 2 - (a/ai)2. For a reduction in loading by a factor of 3, a 6 cm aperture window would be sealed at a 10 cm radius. This decrease in load would allow a factor of (3)1/2 or 1.7 times thinner window. Strengthened windows would lead to a similar reduction in window thickness, and the effects would be additive. The cantilevering effect, added to the strengthening, appeared to accurately predict the experimental results in the NASA program.
Standard flexing disk theory can analytically describe the response of a disk for the case of a fixed edge (location and slope), or a disk with moments imposed at the edge. These boundary conditions do not usually correspond to actual experiments, since perfect clamping requires large forces, and edge moments cannot usually be measured. Equation 1 may also not be appropriate because the maximum stress may no longer be at the center of the disk. The fully clamped edge condition does, however, provide a limits for the maximum stress in the disk for linear theory. At the center of a thin flexing disk with a fixed edge and uniform load Eq. 1 becomes
σ r=0 = 0.47qa2/h2
with higher stresses at the edge of the disk:
σ r=a = 0.75qa2/h2
Even at the edge, the maximum stress in the disk has been reduced by 40% for the clamped-edge boundary condition compared with the free edge boundary condition. The boundary conditions for a disk under pressure sealed with an O-ring is somewhere between these two limits. The actual boundary condition for this case is closer to the edge clamped boundary condition for an O-ring diameter that is much larger than the aperture diameter, but closer to the simply supported boundary condition for an O-ring diameter that is not much larger than the aperture diameter. As will be shown below, the difference in the predicted peak stress in the disk between these two boundary conditions changes significantly in large deflection theory.
Membrane Effects. During testing of thinner (< 1 mm), large diameter (> 50 mm) disks even larger reductions in peak stress were deduced from failure strength, compared with the cantilever effects of thicker disks. Research into the modeling of very thin large disks led to the realization that membrane effects were important.