Aluminization Research for the Large Binocular Telescope

Barry A. Sabol, John M. Hill

Steward Observatory, University of Arizona

Tucson, AZ 85721

and

Bruce Atwood, Paul L. Byard, Tom P. O'Brien, Jerry A. Mason

The Ohio State University, Department of Astronomy
5040 Smith Lab, Columbus, OH 43210-1106

Large Binocular Telescope Project
Technical Memo

UA-93-05
September 1993
http://medusa.as.arizona.edu/lbtwww/tech/ua9305.htm

ABSTRACT
1. INTRODUCTION
2. CRYOPANEL
3. PUMPING ARGON AND H2 WITH THE CRYOPANEL
4. H2 PRODUCTION DURING EVAPORATION OF ALUMINUM
5. ALUMINIZATION IN HIGH PRESSURE H2 AND ARGON
6. SAMPLE H2 CALCULATION FOR THE LBT
7. REFERENCES
LIST OF FIGURES

ABSTRACT

The pumping characteristics of a low-cost activated charcoal cryosorption panel are presented for potential use in the primary mirror, in-situ aluminization system of the Large Binocular Telescope (formerly called the Columbus Telescope). The capabilities of this panel exceed those of the diffusion pump of our test system for most constituents, especially for water vapor. The high levels of H2 produced in the aluminum-H2O reaction, which are pumped by the cryosortion unit to roughly half the amount emitted, are found to be nondeleterious to reflective quality and controllable through proper design geometry. Descriptions of the experiments, cryopumping behavior, and H2 production from glass and aluminum substrates are provided. A sample calculation for the LBT system puts the H2 level in the bell jar near 1.0x10-4 Torr (ionization gauge pressure) during aluminization. This pressure range had no adverse effect on coating reflectivity in our experiments and may provide a convenient smoothing effect to the thickness profile due to low level scattering.

1. INTRODUCTION

Many of the issues concerning the aluminization of the 8.4 meter primary mirror of the LBT are described in earlier reports1-3. The research effort that initially addressed some of these issues was conducted by the Astronomical Instrumentation Facility (AIF) of the Ohio State University Department of Astronomy. Left in limbo after OSU's 1991 withdrawal as a full partner in the project, aluminization research at OSU was again funded for six months by Steward Observatory, University of Arizona. The research has now reached the point of satisfactory completion of initial objectives. New areas of interest have emerged during the course of these studies but the "proof of principle" has been demonstrated.

This report characterizes the low-cost activated charcoal cryosorption panel as the high vacuum pump for a coating chamber and addresses the novel aluminization conditions that are unique to cryosorption pumping. H2, produced in the chemical reaction of freshly deposited aluminum and water vapor, becomes a dominant constituent in pumpdown from rough vacuum pressures and is produced in large quantities (pressures in the 10-4 Torr range) during aluminization. We also include the results of earlier tests using a DP pumped system (reported elsewhere2). More detailed studies of the effect of the Al + H2O reaction on the morphology of aluminum films can be found in the literature4-7.

The content of this report was selected to aid future testing of the LBT system by including tables and graphs for comparison and to provide the modeling information necessary for the design of the LBT coating system. This report was taken from a more complete experimental report8 to which we often refer.

2. CRYOPANEL

When LN2 cryosorption pumping was first introduced as a candidate for the high vacuum pump of the LBT coating system, there were many unresolved issues.

Although zeolite was the preferred sorption material because of its superior pumping characteristics, it requires an extended heating to 300 ° C for regeneration. This would, in turn, require either a large scale in-situ heating system or the construction of an external oven. In addition, there is a corresponding restriction on the melting temperature of solders used in the construction of the panels.

The alternative sorption material, activated coconut charcoal, also has good pumping characteristics and regenerates at room temperature. There are concerns, however, over explosive properties that could develop if the panel adsorbed large quantities of O2.

Finally, the main concern is that of aluminizing in a relatively high pressure of H2 (10-4 torr range) due to the rather limited ability of either sorption material to pump the H2 produced by the aluminum-H2O reaction.

In early 1992, construction of an activated charcoal cryopanel was completed. Initial tests showed the cryopanel pumping down to 1.0x10-6 torr in 30-40 minutes from a 30 mTorr rough vacuum. Two initial aluminizations gave reflectivities as good as our best DP aluminizations even though the chamber pressure continued to rise well into the 10-4 torr range during the shot (as expected) because of H2 production.

In the next phase, the possibility of combustion of the activated charcoal was tested before and after adsorption of oxygen. Although no such problems were expected under normal operating conditions, there was concern over the potential for explosion or disruptive combustion in the event of a major leak. As will be described in a later section, we were unable to ignite the charcoal even after immersion in liquid oxygen.

With these encouraging results, the activated charcoal cryopanel became the test pump for the LBT coating system and we commenced thorough studies of its pumping capabilities before and during aluminization.

2.1 Description

The activated charcoal cryopanel constructed by AIF for the 300 liter coating system consists of (Figure 1) a 8"x18"x.125" (1.0 sq.ft.) OFHC copper plate soldered to 3 parallel .5 inch copper pipes. The pipes are teed into .75 inch copper fittings on the top and bottom. The LN2 is fed into the bottom. The plenum at the top helps to ensure that the lines are full before there is any LN2 outflow.

Approximately 66 grams of activated coconut charcoal were glued onto the copper plate using Crest 3170 epoxy. Stainless steel flexible tubing connects the copper pipe fittings with the LN2 bell jar fittings. A detachable copper chevron cover is mounted over the plate. The entire cryopanel assembly is supported on a stand in an upright position at one end of the bell jar.

2.2 Degassing the Panel

When the warm cryopanel is put under DP vacuum in order to look at the evolved residual gases, it becomes clear that it adsorbs room air. Figure 2 shows the RGA trace of the warm panel which had been sitting out in room air for a few days before pumpdown. Besides H2O (amu 17 & 18), which it readily absorbs in quantity depending on the humidity, the panel has a definite affinity for acetone (amu 43 & 58) which was often used to clean vacuum fittings.

Steambath - One way to achieve a thorough degassing of the panel is through the use of steam. With the panel under DP vacuum, steam is fed into the LN2 exhaust port from a boiling container of water for 2-3 hours. The process is monitored on the RGA. Figures 3 and 4 show the RGA bargraphs during the steambath and again a room temperature (a small air leak developed in the flexible tubing during the steam cycle).

We did not study the pumping performance of the panel before and after the steambath but believe that a steambath should be done: 1) after construction of the panel (soldering and flux fumes, machine shop vapors,etc.) and 2) before use if the panel has been out in room air for an extended period.

2.3 Pumping the Bell Jar from Rough Vacuum

Typical pumpdowns from 30 mtorr and 300 mtorr rough vacuums are shown in Figure 5. The chamber pressures were taken from the thermocouple gauge when P > 1 mtorr and from the ionization gauge when P < 1 mtorr.

There is a fast drop in pressure during the first minute or so after LN2 turn-on. This is due to H2O and CO2 freezing out of the chamber air. The pressure then levels off until 5-8 minutes after LN2 turn-on when the activated charcoal becomes cool enough to pump. Once the charcoal "turns on", the pressure drops very rapidly for a minute or two and then begins a slower rate of descent at about t = 10 minutes.

The higher ionization pressure in the pumpdown from 300 mTorr is due to hydrogen at the 10-5 Torr level. The dependence of H2 levels on the roughing pressure is shown in an RGA trace (Figure 6) for a similar pumpdown from 200 mTorr. The "strange" initial trace behavior is due the detector beginning its scan in a saturated mode.

High H2 Levels - Our explanation of the high H2 levels (which are orders of magnitude higher than atmospheric percentage) is based on our knowledge of H2 production during aluminization. We believe that because our chamber is well coated with evaporated aluminum, the same Al+H2O reaction that takes place with freshly evaporated aluminum is going on with the older aluminum. When the chamber is put under vacuum, H2 is continually produced at a rate that depends on the water absorbed in the chamber walls or the H2O outgassing rate. Since the panel pumps H2 in a manner that provides an "extended volume" (explained in Sec. 3.3), the level builds to an equilibrium determined by the H2O and the extended volume (about 2.5 x belljar volume). When the DP is valved in briefly to pump out this excess H2, we see the level build again to a value that is proportional to the H2O partial pressure at the time. This is so similar to the process during aluminization that it must be the same mechanism.

The important implication of this phenomenon to aluminizing the LBT is that the ionization gauge stops giving pertinent information about the pumpdown once the H2 level is dominate. Since the H2O partial pressure influences coating quality, it seems mandatory to monitor the pumpdown with an RGA.

2.4 H2O and Other Constituents

RGA bargraphs of residual gases are shown for 60 minutes of cryopumping from 100 mtorr (Figure 7) and 165 minutes of cryopumping from 30 mtorr (Figure 8). The contaminants of Figure 2 have been frozen out. We note the following: 1) amu 3 is an RGA artifact, 2) the appearance of amu 4, which is helium left unpumped from the rough pressure (compare with Figures 2 & 4), 3) amu 20 is neon in this trace but is something else in Figures 2 & 4 (verified in combined DP and cryopanel pumpdowns), 4) argon is barely visible because it, unlike helium and neon, is pumped efficiently by the cryopanel (see Section 3). The cryopumping of argon was studied in some detail because of its relatively high percentage in the atmosphere and potential use in glow discharge cleaning9.

2.5 Combustion Tests

Concerns had been raised about the risk of explosion of the charcoal in a worst case bell jar failure - exposure of the cryocooled charcoal to atmosphere resulting in adsorption of large quantities of oxygen, possibly followed by exposure to an ignition source, such as an electric discharge. The experiments described here show the activated charcoal to have no flammability risk in the tests performed.

The activated charcoal used was from the same container as that used on the cryopanel. Single pellets (approx. 4 cu. mm in size) were epoxied to a capped copper pipe. The ignition source in all cases was a spark from copper wire to the charoal on the grounded pipe. The voltage source was a transformer providing 5000V AC. Room humidity was 26% (+-4%).

1) A room temperature test showed no change in the charcoal, either with short, pulsed sparks or continuous arcing (at least 5 seconds).

2) Two tests were done at cryotemperatures. The tube was kept filled with LN2 while first water frost appeared, then oxygen condensed (the oxygen condensate was tested with a paper tissue wetted with the condensate, and then lit. It flared dramatically, confirming that the condensate was oxygen). The tube was angled in such a way that the oxygen condensate ran to the charcoal pellet, which was observed to be uniformly wetting. After approx 10 seconds of wetting the charcoal, a spark was applied directly to the surface of the charcoal, first in bursts, then in a sustained arc. No change in the charcoal was observed in either case.

3) As a final test, individual pellets of charcoal were heated with a butane torch. The pellets glowed orange while heat was applied, but quickly cooled to room temperature when removed from the flame (after less than 3 seconds, they could be held in the hand). A pellet wetted with oxygen condensate flared briefly when held in the flame, but was otherwise unchanged.

Based on these experiments, it would seem that the danger of combustion or explosion of activated charcoal in a belljar failure is zero. The charcoal pellets tested are remarkably nonignitable in the tests performed, even in the presence of pure oxygen.

3. PUMPING ARGON AND H2 WITH THE CRYOPANEL

Several different techniques were used for analyzing the pumping characteristics of the cryopanel. All used either bottled H2 or argon with copper tubing from the regulator to a needle valve. Opening the needle valve either introduced the gas directly into the belljar or into a "reservoir" for later release into the belljar.

Data is designated corrected or uncorrected depending on whether the ionization gauge correction has been applied. The corrections are:

True H2 pressure = 2.4 x ionization gauge reading
True Ar pressure = .83 x ionization gauge reading.

3.1 Reservoir

In order to introduce known quantities of gas into the belljar for cryopanel pumping tests it became necessary to employ a "reservoir". The reservoir was a spare CCD dewar with Convectron gauge tube attached. Its volume was calculated to be 5.4 liters including the flexible tubing and valve assemblies. The belljar volume is 298 liters so that the ratio of reservoir volume to belljar + reservoir is .018.

Procedure - The belljar + reservoir (cryopanel warm) were pumped out for a few hours until the outgassing rates were very low (90 seconds to leak up to 1.0x10-5). Since most experiments would be done in the 10 -4 range, this leakage was negligible. The reservoir was filled to various pressures (say, 20 mtorr, 40 mtorr, etc.) and released into the chamber. The pressures at 60 and 90 seconds were recorded. This proved to be repeatable. It was also found that 99% of the pressure rise occurred in 60 seconds. The maximum pressures (at about 90 seconds) were used as the initial pressure rather than those calculated from dewar volumes and gauge corrections.

For some experiments the pressure rise after release was monitored in time by computer both with and without cryopanel. These data are the most directly applicable to our goal of knowing and predicting the H2 pressure during aluminization.

Check - When the results for several warm cryopanel reservoir releases were averaged and the gauge corrections employed, they yielded a reservoir/reservoir+belljar volume ratio of .021; to be compared with the calculated value of .018.

3.2 Pressure Drop Due to Cryopanel Cooling

When the gas is released from the reservoir one can expect some pressure drop due to cooling rather than pumping.

The area of the cryopanel (both sides) is 2 sq. ft. or 1858 cm2. If this value is inflated by a factor of about 1.5 to accomodate the chevron assembly, pipes, and the greater area of the charcoal, the effective area is 2.7x103 cm 2.

The surface area of the belljar is 2.7x104 cm2 so that the ratio of cryopanel to belljar area is 0.1.

With the panel temperature at 77 K and the belljar at 295 K an average temperature could be calculated as:

Average Temp = (0.1 x 77 ° K + 1.0 x 295 ° K) / 1.1 = 275 ° K

This gives a 20 K difference out of 295 K or about 7%. Calculating pressures from the ideal gas law also gives a 7% reduction due to cooling.

This effect is shown in Figure 9. Here, 60 mtorr of H2 in the reservoir was released into the belljar with the cryopanel warm. When the pressure (uncorrected) came to equilibrium, the LN2 flow was started. The chamber was very well pumped out so that very little of the pressure drop was due to water and/or CO2 freezing out. The pressure declines slowly until the charcoal "turns on". The expected 7% drop due to cooling is plotted and seems to be consistent with the data.

3.3 Extended Volume Model

The cryosorption pumping of some constituents is often characterized in terms of "extended volume". For our purposes this means that when a known quantity of gas is bled into a chamber with cryopanel, the new equilbrium pressure is found from the quantity of gas and the extended volume which is the chamber volume + residence volume of the cryopanel. The extended volume is fairly constant over a wide range of pressures. For example, if 10-3 torr-liters were released into a 10 liter bell jar (no cryopanel) the pressure would rise to 1.0x10-4 torr. If there were a cryopanel and if the new pressure were 2.0x10-5 torr, the extended volume would be 5 times the bell jar volume. A different quantity of gas released would still result in a belljar with cryopanel pressure that is 5 times less than that without cryopanel (if the extended volume is constant over this range).

This concept is used in the H2 pumping section to quantify the capabilities of our design.

3.4 Argon Pumping

Adsorption Isotherms - There are many ways to characterize the pumping of a cryopanel depending on the eventual application. Adsorption isotherms are commonly used and are found by leaking in known increments of gas and recording the equilibrium pressure after each increment. Usually, the equilibrium pressure is the x-axis and the y-axis gives the cumulative total gas released per gram of sorption material (torr-liters/gm). Since it may take some minutes or even hours to reach an equilibrium pressure, this method has limited use.

Our argon pumping data is presented as adsorption isotherms even though 1) it is a patchwork of different reservoir pressure releases at different times and 2) the time to "equilibrium" varies from 5-10 minutes. Figure 10 gives these isotherms.

Glow Discharge Cleaning with Argon - A test was conducted to determine if the glow discharge cleaning process was feasible in a cryopumped system. Argon was bled into the cryopumped chamber so that the pressure was 5-6 mTorr on the Convectron gauge. This pressure was maintained for 10 minutes (the flow had to be reduced several times). After 10 minutes the flow was stopped. The Convectron pressure after 1 minute was 4 mTorr and after 5 minutes was 3 mTorr. These results preclude glow discharge cleaning with argon in an activated charcoal cryopumped system.

3.5 Hydrogen Pumping

H2 Release prior to Cooling the Cryopanel - Various amounts of H2 were released from the reservoir into the belljar with warm cryopanel. Then the LN2 flow was started and the equilibrium pressure recorded after about 15 minutes of LN2.

Figure 9 (uncorrected pressure), which was discussed earlier to demonstrate the 7% cooling effect is one such test. Typically, the equilibrium pressure is 35-45% of the unpumped pressure.

Continuous H2 Leak - The extended volume concept of cryopumping is clearly shown when H2 is leaked into a chamber at a known rate. The procedure was to pump out the belljar thoroughly with the DP (so that the outgassing rate was very low) then, with belljar closed, adjust the needle valve until the pressure rise from H2 leaking at a constant, manageable rate. At this point the needle valve was left in that position, the DP valved back in, the LN2 to the cryopanel turned on, and after 7 minutes (time for the charcoal to turn on), the DP valved off.

Figure 11 shows the slower of two H2 leak tests which was (uncorrected) 2.44x10-6 torr/sec (cryopanel off) to 9.44x10-7 torr/sec (cryopanel on) corresponding to an extended volume of 2.70 times the bell jar volume.

Pump Response to a Sudden H2 Pressure Difference - In an attempt to simulate the behavior during aluminization we have conducted several tests where the H2 pressure is monitored for 60 seconds following a sudden release. Each test compares a release into the closed chamber with cryopanel warm with an identical release into the closed chamber with cryopanel cold.

Figure 12 gives the average of two such tests that released an H2 reservoir pressure of 100 mtorr. Figure 13 gives the H2 pressure reduction fraction due to cryopumping for an average of several of the above tests. This is H2 pressure with cryopumping divided by H2 pressure without cryopumping. At later times, the reciprocal of this quantity is the extended volume factor.

Cryopanel Residence Volume for H2 - The extended volume is the chamber volume + the residence volume for H2 of the cryopanel.

Vext = Vch + Vcryo

For a given amount of H2 injected into a chamber+cryopanel at negligibly low pressure

H2(torr-liters) = Pch x Vext

Let f be the pressure reduction fraction of Figure 13.

Then Vext = Vch / f

and Vcryo = (1/f - 1) x Vch

For our cryopanel design we want the cryopanel residence volume per square meter of panel surface area:

Vcryo-area = 300 liters x (1/f - 1) / 9.3 x 10 -2 m2

or Vcryo-area = 3230 x (1/f -1) liters/m2

4. H2 PRODUCTION DURING EVAPORATION OF ALUMINUM

Previously1, we described a phenomenon known as "blue haze"10 which, for DP pumped systems, shows up as a sharp pressure rise, indicating a surge of gas, and can reportedly swamp the smaller pumps and ruin the aluminum coating.

From the nature of the pressure rise (as seen on the ionization gauge of our DP pumped system), which commences with evaporation and diminishes in a few seconds, we concluded that there was a shortlived surge that swamped the DP, followed by a second phase of lower production rates with which the DP was better at keeping up. Of major concern was the possibility that our proposed cryosorption scheme may pump these constituents at a lower speed or not at all. To investigate this phenomenon and to understand generally the evolution of gases during evaporation, we purchased the residual gas analyzer (RGA).

The dominant gas involved was found here and elsewhere11 to be H2. It is a product of the evaporated aluminum reacting with water vapor. Only a small portion of the H2 produced is from the reaction of fresh aluminum with the free water vapor in the chamber. Most of the H2 is emitted from the freshly coated chamber walls and substrate where water vapor resides on and within the surface. The reaction involved is believed to be:

2Al + 3H2O > Al2O3 + 3H2.

Progress in our early experiments was hindered by the limitations of the RGA. The RGA response was found to become nonlinear at pressures of 3x10-5 Torr and saturated by 4x10-5. This limitation appears to be independent of adjustments of the emission current or sensitivity.

In addition to knowing where and when to use the RGA, we now monitor the ionization gauge pressure, filament voltage and current, and deposition rate on computer. We have refined our techniques to discriminate between H2 production from coated metal and clean glass. We know what to expect in both DP and activated charcoal cryopumped systems.

4.2 H2O Partial Pressure Behavior during Pumpdown

Since H2 is produced in the reaction of aluminum with water vapor, we discuss the behavior of H2O during pumpdown.

Both DP and cryopumped (unbaked) chambers behave in the following manner when pumped own from atmosphere. After about an hour of pumping, the pressure declines slowly because the rate at which gases are pumped out equals the rate at which they are being outgassed into the chamber from the surfaces. It is the outgassing rate that decreases over time and, consequently, allows the pressure to come down. Since H2O is abundantly present within the surfaces of the chamber, the constituent with the highest partial pressure is H2O (except for H2 in the cryopumped system).

The type of material on the surface of the chamber, how long it has been exposed to atmosphere, and the humidity are all factors that contribute to the H2O outgassing rate. Although our chamber has stainless steel walls, they are covered with evaporated aluminum with oxide layers. The oxide, Al2O3, is known to absorb water readily.

Measurements of outgassing rates are notoriously difficult to make. We believe that our measurements of the very high H2 outgassing rates (in our DP aluminizing tests) were successful but have no faith in the low H2O rate measurements. Consequently, the parameter that best represents the state of the H2O outgassing rate is the H2O partial pressure at anytime (because the pumping rate equals the outgassing rate). For evaporation tests, we take the H2O partial pressure immediately prior to the shot as an indicator of the H2O outgassing rate.

Activated Charcoal vs. DP Pumped Systems - There are some differences that should be noted. Because of the size of our cryopanel, the H2O pumping speed is much higher than that of the DP + cold trap. The H2O partial pressure is still an indicator of outgassing rate but the correspondence is not the same as the DP case. We cannot directly connect the results of an aluminization in the cryopumped system with one in the DP pumped system on the basis of H2O partial pressure.

When it comes to the well known12,13 dependence of coating reflectivity to H2O partial pressure, however, the cryopanel and DP pressures have the same meaning. This effect is dependent upon the free H2O in the chamber of which the H2O partial pressure is a direct measure.

The other difference in H2O behavior with the DP system is the high levels of H2 present during a cryopanel pumpdown. They are discussed in detail in the Cryopanel section.

4.3 H2 Evolution during Aluminizing - DP SYSTEMS

As noted elsewhere, the sharp pressure surge observed during aluminization is due to H2 produced from the reaction of the fresh aluminum with the water on the walls of the chamber. Careful observation has shown that as soon as the thickness monitor registers deposition, the pressure rise begins.

After monitoring many aluminizing runs with a residual gas analyzer, we have identified two distinct hydrogen production regimes. The initial rapid evolution of hydrogen, the result of the reaction of fresh aluminum with H2O on surfaces within the chamber, produces the H2 peak seen near t=0 in both Figures 14 and 15. The peak pressure is well above the saturation value of the RGA and is known (from the ionization gauge) to be in the 10-4 Torr range.

Hydrogen then continues to be produced at a lower rate for a time which depends on the H2O partial pressure before evaporation, and therefore on the rate that H2O arrives on the surface from the interior of materials within the chamber. (In these shots the coated area is not precisely known - only that it is over half the chamber surface area of 2.7x104 cm2.) Figures 14 and 15 compare the high and low initial H2O partial pressure cases. Note that as the reaction ends, approximately at the time indicated by the dotted vertical line, the O2 partial pressure begins to rise, indicating that the available aluminum has been consumed and that the Al2O3 film has been formed.

That both the peak and the later behavior are surface area effects is easily verified. Figure 16 shows an initial smaller H2 peak where a shutter confined much of the vapor followed by a larger peak occurring when the shutter was opened.

Figure 17 plots the time for the reaction between Al and H2O to finish as a function of initial H2O partial pressure. The total amount of H2 is nearly independent of the initial H2O partial pressure and is roughly linearly dependent on the total area coated with aluminum.

4.4 H2 Evolution during Aluminizing - CRYOSORPTION SYSTEM

In contrast to the short-lived H2 pressure surge in the DP shots, the pressure in a cryopanel aluminization rises at once to a high level and continues to rise at a more gradual rate. Figure 18 shows the ionization gauge pressure and filament power over time in one such shot. The ionization gauge reading was 5.6x10-4 right after the shot and had risen to 8.3x10-4 by 4 minutes after the shot. (The area coated here is unknown - roughly half the chamber area - cryopanel was shielded.)

This behavior was anticipated from the results of the DP shots and the knowledge that activated charcoal pumps H2 poorly. From the H2 pumping results of the Cryopanel section, we know that the H2 level observed here is roughly half of that produced.

The amount of H2 present in this aluminization was sufficient for scattering (see Scattering section) and a faint film was observed on the backs of the substrates coated.

Reduced Area Experiments - Glass and Aluminum Lined Beakers - In order to study H2 evolution in a controlled environment for the purpose of obtaining modeling parameters, a set-up with reduced coating area was employed.

In this set-up (Figure 19), the filament and mounting assembly were enclosed in a 4 liter Pyrex beaker. The beaker was supported .25 inches from a flat platform to allow the evolved gas to escape. This set-up was used in two ways: 1) Aluminizing Clean Glass - In this case the beaker, glass platform, and glass supports were stripped and cleaned in the manner of astronomical mirrors (i.e. HCl+CuSO4, KOH+CaCO3, and HNO3 solutions with distilled water between steps and after).

2) Aluminizing Aluminum - Here, the beaker was lined with aluminum foil, the platform was sheet aluminum that had been coated many times, and the glass supports were wrapped with aluminum foil.

In both cases the coated area was 1660 cm2. A low aluminum cylinder sat on the platform surrounding the beaker to stop any stray aluminum vapor that may have scattered out of the .25" opening. This potential coating area and a small portion of the filament assembly were the only aluminum areas in the clean glass shots.

Presented here are two separate runs of "beaker shots", each with a pair of glass and aluminum coatings at similar low H2O partial pressures and a pair with higher H2O partial pressures. The two runs took place under different procedures which may account for some differences in the data. The procedures are:

1st Run - The chamber + warm cryopanel was pumped from rough vacuum for about an hour with the DP. The cryopanel was then cooled and both pumps operated until the desired H2O partial pressure was reached. The DP was valved off while recording the H2O partial pressure (this proved to be inaccurate) and valved back in while warming up the filament at 30% on the variac (the shot took place at 60-70%) to remove the excess H2 from warm up. At this time the DP was valved off and the beaker aluminized.

The higher H2O partial pressures of the 1st run include pluses (+) to indicate that the value could be misleading, and as an indicator of H2O content or outgassing, it is probably too low. This value was recorded right after the DP was valved off. If more time had been allowed to elapse, the value would have risen to a more accurate indicator of the outgassing rate for the cryopanel + chamber (as do those of the 2nd run). This behavior was verified in RGA traces where the H2O partial pressure is still rising when the shot is taken. The effect shows up in the results of CR44 and CR45.

2nd Run - The DP was never used in these tests. The cryopanel pumped the chamber down from rough vacuum until the desired H2O partial pressure was reached.

The shots and figures are listed below (pressures in Torr).

Figure Shot AMU 18 (H2O) Comments
1st Run
32&33 cr42 4.25E-7+ Clean Glass
34&35 cr44 4.03E-7+ Aluminum
36 cr45 3.56E-7+ Aluminum
37&38 cr46 3.78E-7+ Clean Glass
39 cr47 5.50E-8 Aluminum
40&41 cr48 8.42E-8 Clean Glass
42&43 cr49 1.14E-7 50 min after CR48
2nd Run
44 cr54 3.19E-7 Aluminum
45&46 cr55 3.14E-7 Clean Glass
47 cr56 1.01E-7 Aluminum
48&49 cr57 9.84E-7 Clean Glass

Figure 20 (CR46) gives the ionization gauge reading during the coating of a glass substrate. The filament power is also included. Note that in this run the DP was on during the filament warm- up (t = 0-19 sec, power is up, pressure is low). While the onset of H2 production coincides with the rise in filament power to vaporizing temperatures, the change in production rate ( t = 23 sec) occurs before the power decrease.

The associated RGA trace (Figure 21) is much smoother due to some noise source with the ionization gauge. Note the good agreement with RGA amu2 and the ionization gauge reading. Unfortunately, the RGA response becomes nonlinear around 3x10-5 torr.

A much higher level of H2 accompanies a shot with aluminum substrate at a similar H2O partial pressure. Figure 22 (CR54) shows the filament warm-up (plateau region t = 30-50 sec).

4.5 H2 Produced in Filament Warm-up

Much of the H2 that appears during filament warm-up is released when the filament is "red" and not at the melting temperature of aluminum. On our power supply, this occurs with the variac at about 30% while the evaporation takes place at 60-70%. The amount produced from our 4x.030 tungsten filament was found to range from 3.0x10-3 to 9.6x10-3 torr-liters (corrected pressures).

4.6 Regeneration?

- Shot CR49 (Figure 23) was taken 50 minutes after CR48 without opening the chamber or pumping again with the DP (evaporation in CR48 ended before the filament went dry). This test was done for the express purpose of verifying that the majority of the H2 comes from the Al + H2O reaction and not from the filament and that it takes longer than 50 minutes for the H2O to regenerate in and on the surfaces.

4.7 t < 3 seconds, h2 Surge in Reduced Area Tests

H2 "Surge" - As a result of our H2 evolution work on DP pumped systems we speculated that the intial H2 peak or "surge" was a separate production process because of its high rate compared to later H2 production. We put forth the idea that the peak was caused by the first arriving aluminum reacting with the water on the surface.

The "beaker shots" give us the opportunity to examine the early H2 production and to test its dependency on initial H2O partial pressure, and material (aluminum or glass), although it should be noted that the "beaker set-up" may retard the pressure changes during aluminization. Our data during the first 5 seconds of the shot appears to be consistent, however, so that any retardation is probably negligible.

We analyze the first 5 seconds of the shots of the 1st and 2nd Runs using the RGA data logs. The starting point, t=0, is chosen to be the time when the pressure changes by about 2x10-6 torr in 1.0 second. For the 2nd Run this point is at the end of the 30% warm-up "plateau". The following quantities are given below:

Shot#, material, and H2O content; pressure change in 5 seconds in Torr (delta), and four rates over 2 second periods in Torr/sec with each period 1 second apart: R(0-2), R(1-3), R(2-4), and R(3-5). The first is from t=0 to t=2, the second t=1 to t=3, etc.

Shot (delta) R(0-2) R(1-3) R(2-4) R(3-5)
44A-H+ 2.19E-5 6.17E-6 7.25E-6 3.85E-6 2.05E-6
45A-H+ 2.96E-5 1.03E-5 8.05E-6 3.55E-6 2.05E-6
54A-H 1.48E-5 4.16E-6 3.95E-6 2.40E-6 1.70E-6
47A-L 1.60E-5 4.82E-6 4.58E-6 2.25E-6 1.70E-6
56A-L 1.44E-5 3.35E-6 3.55E-6 2.95E-6 2.25E-6
42G-H+ 1.05E-5 2.93E-6 2.30E-6 1.44E-6 1.50E-6
46G-H+ 1.36E-5 4.26E-6 3.41E-6 1.85E-6 1.35E-6
55G-H 8.95E-6 2.48E-6 2.20E-6 1.50E-61.15E-6
48G-L 1.11E-5 3.02E-6 3.22E-6 2.23E-6 1.15E-6
57G-L 1.04E-5 2.20E-6 2.40E-6 2.05E-6 1.90E-6

Discussion:

a). There is clearly more H2 produced from aluminum than glass.

b). The most revealing quantities are R(0-2) and R(1-3) which are the rates of H2 production over 0-2 seconds and 1-3 seconds.

c). In most cases the rate falls off after R(1-3) (dramatically in the A-H+ shots).

d). The H2 production rates are higher in the 1st Run than in the 2nd. Whether this is due to the difference in procedure or just a different week with different humidity is unknown.

e). If the 2nd Run is viewed independently, there is no correlation between H2 production and H2O partial pressure.

Conclusions:

The "surge" or extremly high rate of H2 production lasts from 2-3 seconds after deposition begins. The short time duration would seem to indicate that it is associated with H2O on the substrate surface. The production rate is considerably higher for an aluminum substrate as opposed to clean glass (higher microscopic surface area and more absorption of water by the oxide layer). The production rate is probably higher for higher H2O partial pressures (at least if over a certain threshold).

Below, we average the 5 second pressure change and the four 2 seconds rates into 3 categories: Al-High, Al-Low, and Glass by letting H+ = H and noting very little difference between H2O high and low for glass.

Average Rates of H2 Pressure Increase Over 1st Five Seconds
CORRECTED PRESSURES

Mat.&H2O Del P (5s)
Torr
R(0-2)
Torr/sec
R(1-3)
Torr/sec
R(2-4)
Torr/sec
R(3-5)
Torr/sec
Al Med-Hi 2.21E-5 6.88E-6 6.42E-6 3.27E-6 1.93E-6
Al Lo-Med 1.52E-5 4.09E-6 4.07E-6 2.60E-6 1.98E-6
Glass 1.09E-5 2.98E-6 2.71E-6 1.81E-6 1.41E-6

4.7 t > 3 seconds, Reduced Area Data throughout Aluminization

Having looked at the first few seconds of the reduced area depositions to verify our understanding of the process, we now concentrate on H2 production during the rest of the shot. The bell jar H2 pressure, which may affect coating reflectivity if too high, is of particular importance to the point spread distribution of deposition because of scattering.

H2 Produced in Reduced Area Shots - Again, the shots are sorted into categories by substrate material and H2O partial pressure, then averaged. The groupings are:

Aluminum Lo-Med Residual H2O CR 47, 54, 56 Figure 24
Aluminum Med-Hi Residual H2O CR 44, 45 Figure 25
Glass Lo-Med Residual H2O CR 48, 57 Figure 26
Glass Med-Hi Residual H2O CR 46, 55 Figure 27
The lower curve in each figure is the amount of H2 in the bell jar at time t for every square centimeter of substrate area. The upper curve is the cumulative H2 produced at time t per sq. cm of substrate area (i.e. the amount that would be seen if no cryopanel). The upper curve is formed by folding the H2 pressure reduction fraction (Figure 13) into the lower curve. The initial H2 levels and levels due to filament warm-up have been subtracted out. The ionization gauge correction (2.4 x gauge reading) has been included in both curves.

There is clearly a large difference in H2 output between aluminum and glass substrates and a smaller distinction for differences in H2O partial pressure. For example, by t = 30 seconds, the aluminum substrate has produced about 7 times more H2 than the glass substrate. Looking at the difference in H2 produced for the two H2O partial pressures in the same material, we find this difference to be a factor of 10 higher for aluminum. One can speculate that this difference, for glass, is mostly due to the difference in the free H2O of the bell jar reacting with the film surface.

Note on Oxide Formation in Reduced Area Shots - We can use the cumulative H2 amounts of Figures 24-27 to calculate the thickness of the oxide layer formed. The reaction involved is believed to be 2Al + 3H2O > Al2O3 + 3H2. One molecule of oxide is formed for every 3 H2 molecules released.

Measurements done elsewhere14,15 have used the degradation of UV reflectance to find the thickness of the oxide film formation in vacuum. Also, oxide formation on the microstructual scale is examined in the literature4-7. In our case, however, the oxide film is not necessarily confined to the exposed surface. In fact, a significant fraction may be formed in the substrate- film interface. Therefore, the calculation (given elsewhere8) may be of academic interest only.

From the values of the upper curves (Figures 24-27) at t = 60 seconds

Aluminum Substrate Lo-Med H2O Oxide Thickness = 7.6 angstroms
Aluminum Substrate Med-Hi H2O Oxide Thickness = 10.8 angstroms
Glass Substrate Lo-Med H2O Oxide Thickness = 1.2 angstroms
Glass Substrate Med-Hi H2O Oxide Thickness = 1.95 angstroms

5. ALUMINIZATION IN HIGH PRESSURE H2 AND ARGON

5.1 Test Slides from Cryopanel Aluminizations (H2 only)

Two shots, CR19 and CR20 were taken after pumpdown by the cryopanel to respective H2O partial pressures of 4.2x10-7 and 2.9x10-7 Torr. 910 angstroms of aluminum were deposited in each shot at a rate near 40 ang/sec at a distance of 33 cm from the filament. The ionization gauge readings right after the shots were (these shots preceded the installation of the pressure logging hardware) 4.7x10-4 and 7.0x10- 4 Torr. These H2 pressures are somewhat excessive for this sort of shot because the cryopanel chevron was not shielded from the source. A transparent film was formed on the back of the slides due to scattering. The high H2 pressure apparently did not have an adverse effect on the reflectivity (see below and Figure 28).

5.2 Test Slides in Background Gas Flow in DP System

Test slides for reflectivity measurements were produced in a run of 8 shots by depositing 1000 angstroms at rates near 40 ang/sec at a distance of 33 cm from the filament. Background gas pressures (corrected) during the depositions were: 8.3x10-5 and 8.3x10-4 Argon, and 1.2x10-3, 2.4x10-3, and 4.8x10-3 Torr H2. Also, there was one baseline shot taken at 1.8x10-6 Torr. Other slides were placed at various locations in the chamber to observe the effects of aluminum vapor scattering.

These tests were done in a diffusion pumped system with the desired background gas pressure maintained by bleeding in bottled H2 and Ar through a needle valve. The H2O partial pressure was read prior to bleeding in the background gas. The shots, background gas pressures, H2O partial pressures, and the mean free path16 are listed below:

Shot Corr. Press. H2O Pressure Mean Free Path
DP25 1.8E-6 Torr 1.01E-6 Torr 278 cm
DP26 8.3E-5 Ar Torr 8.11E-7 Torr 58 cm
DP27 8.3E-5 Ar Torr 6.60E-7 Torr 58 cm
DP28 8.3E-4 Ar Torr 9.16E-7 Torr 5.8 cm
DP29 8.3E-4 Ar Torr 8.78E-7 Torr 5.8 cm
DP31 1.2E-3 H2 Torr 1.01E-6 Torr 7.5 cm
DP30 2.4E-3 H2 Torr 8.99E-7 Torr 3.8 cm
DP32 4.8E-3 H2 Torr 1.00E-6 Torr 1.9 cm

5.3 Reflectivity

The slide reflectivities were measured on the AIF monochromometer over the wavelength interval 300 to 1100 nanometers. The increasing errors near the ends of the interval have been deleted from the traces by presenting the interval 350 to 1000 nanometers.

Figure 28 compares the cryopanel aluminization CR19 and CR20 with book values17.

The slides from the diffusion pumped series are compared with the cryopanel shots in Figures 29-32. The following averages were taken:

1) CR19 and CR20 are averaged and displayed as the "cryo" shot.

2) The reflectivity of the DP series slides were measured soon after the run and again one week later. The results of the two measurements are averaged for each slide.

Results - The cryopanel shots have reflectances very close to the book values. Of the DP series, we are relieved to see that there are no apparent losses in reflectivity due to high background H2 pressures, even for the shot with 1.9 cm mean free path. There do appear to be some problems with shooting in high pressure argon (8.3x10-4) although our tests are not extensive enough to be sure. If real, the problems in the high pressure argon shots may be due to the sort of collisions the aluminum vapor undergoes. For the same value of mean free path in H2 andargon the kinematics are quite different (see Scattering section below).

5.4 Scattering

Additional slides were placed in various locations of the bell jar during the DP series of shots to gain some insight into the scattering of aluminum vapor in background gas.

The slide locations are as follows (see Figure 33): 33S is the source facing test slide that received 1000 angstroms, 33Z is a zenith facing slide on the back of 33S. Similarly, 50S and 50Z were mounted 50 cm from the source. 11-13Z and 11-20Z are mounted on a platform at 11 cm above the source and at a radial distance of 13 and 20 cm from the source respectively and are not in the line of sight of the source.

The coating thicknesses were calculated from transmission measurements18 and divided by 1000 angstroms. So the values given are fractional amounts of the thickness of 33S.

It was found that when the filament power (averaged over the last 15 seconds of the shot) is divided by the deposition rate (similarly averaged) the result (watts per ang/sec of deposition rate) tracks the scattering behavior at 50S. Also at 50 cm, if the source displays 1/R2 behavior, the thickness would be 444 angstroms (we have 455 angstroms for DP25). So the values of 50S are good indicators of the loss over distance due to the vapor following new trajectories not possible in lower pressures and the Filament Power / Dep. Rate indicates the increase in power necessary to maintain the 40 ang/sec rate.

Shot Gas MFP 33Z 50S 50Z 11-13Z 11-20Z Pow/Rate
DP25 - 278 - .455 - - - 8.82
DP26 Ar 58 0 .443 - - - 8.99
DP27 Ar 58 0 .433 - - - 8.96
DP28 Ar 5.8 .309 .261 .069 opaque .294 12.28
DP29 Ar 5.8 .294 .267 .080 opaque .294 11.95
DP31 H2 7.5 .049 .375 .029 .053 .038 9.29
DP30 H2 3.8 .167 .291 .056 .248 .132 10.31
DP32 H2 1.9 .374 .228 .074 opaque .407 13.01

Reflectance of Scattered Slides - the reflectances of the opaque 11-13Z slides were measured and given with that of the associated 33S slide in Figures 34-36. There are no drastic differences here. In fact, the 11-13Z slides shows better reflectivity in DP29. Although this could be an indication of the measurement error, the point is that even after deflections leading to a 180 ° change in direction, the reflectance is apparently unaffected. Certainly a large percentage of the vapor must be coming in at other than normal incidence but either the percentage that is 45-90 ° from normal is small or else the bad effect of this sort of deposition17 is counteracted by the percentage in the 0-45 ° degree range.

Kinematics - A computer program was written to compare the collision properties of H2 with argon. Based on temperature and mass the atoms were given the following speeds: H2 - 1930 m/s, argon - 430 m/s, and aluminum - 1300 m/s. The results (not shown) indicate that the maximum possible deflection of an aluminum atom by an H2 atom is 26 ° with most collisions deflecting far less. Argon, on the other hand, can deflect the aluminum atom in almost any direction because of its greater mass.

Application to Modifications in Thickness Distribution - Elsewhere 1,3, baffling or aperturing the vapor path near the source has been considered as a means of restricting the vapor incidence angle to 0-50 ° from normal. The result of such a restriction, for a large number of filaments in an LBT-like chamber, (Figure 37) is a thickness distribution with too much shadowing structure. Clearly, small-angle scattering (for which H2 is an ideal choice), could smooth this profile. The determining factor in such a case would be the right H2 pressure. In light of the11-13Z reflectances, it may be that aperturing or baffling is not necessary, or if baffling and scattering were used together, that the result may be no different than not baffling.

Enhanced Scattering Near the Source - Filament Shield Considerations - There is a region around the source in which the number density of aluminum atoms is on the order of the background gas densities considered above. When the mean free path of aluminum in the gas is low (as in DP28,29,30,32) and the number density of the aluminum atoms is the same as that of the gas, then aluminum-aluminum scattering can take place. This resembles a "cloud" of scattering near the source and may need to be taken into account in the design of filament shields.

A simple calculation 8 yields the following. Given a point source depositing 40 ang/sec and 100 ang/sec on a substrate located 33 cm away, we want the radial distance from the source where the number density of aluminum atoms equals the number density of gas atoms for the corrected pressures 1.0x10 -4, 1.0x10-3 Torr:

Deposition Rate Pressure Radial Distance
40 ang/sec 1.0E-4 torr 7.8 cm
40 ang/sec 1.0E-3 torr 2.5 cm
100 ang/sec 1.0E-4 torr 12.3 cm
100 ang/sec 1.0E-3 torr 3.9 cm

6. SAMPLE H2 CALCULATION FOR THE LBT

Here, we list the expected contributions to the H2 pressure during aluminization through the use of coated surface areas and the cumulative H2 pressures of the reduced area shots (Figures 24- 27).

The H2O partial pressure levels given in these figures, that influence H2 output, might be interpreted roughly as: Med-Hi - one hour of cryopumping after overnight roughing and Lo- Med - two to three hours of cryopumping after overnight roughing.

Using an 8.4 meter mirror with 1.0 meter center hole in a 9.0 meter diameter bell jar of height 2.0 meters, we assume that the aluminum is confined to the mirror, the annular bell jar face (8.4-9.0 meters), and the filament fixtures and shielding (to shield the rest of the chamber from evaporated aluminum). We also assume that these surfaces produce H2 at the rate of aluminum except for the mirror.

The number of filament assemblies (which turns out to be very important) is taken as 150. Reference 1 gave the number as 255 but these were 2-strand filaments and we have since used 4 strand of a different design that double the capacity. Additional experiments with high- capacity crucibles are now being done at the AIF. The surface area for fixtures and shielding is taken as 1000 cm2 (a little over 1 sq. ft.) for each filament.

H2 produced in the warm-up of one filament was found to average 7.0x10-3 torr-liters (Sec. 4.5).

Surface Areas (cm2)

Bell Jar annulus + center hole = 9.0E4
Mirror = 5.5E5
150 Filament fixtures, shields = 1.5E5

Chamber Volume

= 1.27E5 liters

H2 Produced by t = 30 seconds (torr-liters/cm2)

Aluminum Lo-Med 1.1E-4
Aluminum Med-Hi 1.5E-4
Glass Lo-Med 1.8E-5
Glass Med-Hi 2.3E-5
Contributions (torr-liters) Lo-Med Med-Hi
Bell Jar + Center Hole 9.90 13.50
Mirror 9.90 12.65
150 Filament Shields 16.50 22.50
150 Filament Warm-ups 1.05 1.05
Totals 37.35 49.70 torr-liters

Let us assume that the LBT chamber has 16 m2 of panel area (this is being proposed). At t=30 seconds (which should be near the end of the shot) the pressure reduction fraction from Figure 13 is f = 0.44. From Section 3.5, the cryopanel residence volume is Vcryo = 6.58x104 liters or half the chamber volume. The extended volume, Vext, is 1.93x105 liters.

The bell jar pressure would then be:

Med-Hi H2O Lo-Med H2O
Corrected 2.58E-4 Torr 1.94E-4 Torr
Ionization Gauge 1.07E-4 Torr 8.07E-5 Torr
Mean Free Path 35 cm 46 cm

Note that the above calculations do not include a shutter. The contributions from a shutter arrangement would probably be similar to those of the filament fixtures and shields.

7. REFERENCES

  1. "Evaporative Coating Systems for Very Large Astronomical Mirrors", B.A. Sabol, B. Atwood, J.M. Hill, J.T. Williams, M.P. Lesser, P.L. Byard, W.B. Davison, Feb 1990. Proceedings: SPIE-Adv Opt. Telescopes IV, 1236, 940.

  2. "Studies of Some Aspects of Aluminizing Large Astronomical Mirrors", B. Atwood, B. Sabol, Apr 1992. Proceedings: ESO Conf. on Progress in Telescope and Instrumentation Technologies,ed. M-H Ulrich, 265.

  3. "Notes on Aluminizing 8 meter Mirrors", J.M. Hill, M.P. Lesser, B.A. Sabol. Columbus Project Technical Memo UA-88-06, Aug 1988.

  4. "Effects of Water on the Growth of Aluminum Films Deposited by Vacuum Evaporation", M.J. Verkerk, W.A.M.C. Brankaert, (1986). Thin Solid Films 139, 77.

  5. "Room Temperature Adsorption of Water by Aluminum Thin Films", W.H. Krueger, S.R. Pollack. Surface Science 30, 280, (1970).

  6. "Microstructual Studies of the Growth of Aluminum Films with Water Contamination", G.J. van der Kolk, M.J. Verkerk. J. Appl. Physics 59, 4062, (15 June 1986).

  7. "Work Function Changes Due to the Chemisorption of Water and Oxygen on Aluminum", E.E. Huber,Jr., C.T. Kirk,Jr. Surface Science 5, 447, (1966).

  8. "Aluminization Research: Cryosorption Pumping and H2 Production", B.A. Sabol, et al. July 1993 (Unpublished).

  9. "Glow Discharge Cleaning - Review and Recommendations", B.A. Sabol. MMT Upgrade/Conversion Technical Memo #89-1, Dec. 1989.

  10. . "Aluminizing System Design for the CIW Du Pont 100-Inch Telescope, Las Campanas Observatory, Chile", B. Rule. CIW Du Pont Engineering Report, Aug 1972.

  11. . Vacuum Deposition of Thin Films, L. Holland. John Wiley & Sons, NY, 1956.

  12. . "Filmed Surfaces for Reflecting Optics", G. Hass. J. Opt. Soc. Am. 45, 11, 945 (Nov 1955).

  13. "A Direct Comparison of the Visible and Ultraviolet Reflectance of Aluminum Films Evaporated in Conventional and Ultra-High Vacuum Systems", E.T. Hutcheson, G. Hass, J.K. Coulter. Optics Communications, 3, 213-216, (June 1971).

  14. . "Reflectance-Increasing Coatings for the Vacuum Ultraviolet and Their Applications", P.H Berning, G. Hass, R.P. Madden. J. Opt. Soc. Am. 50, 6, (June 1960).

  15. "On the Vacuum-Ultraviolet Reflectance of Evaporated Aluminum before and during Oxidation", J. Opt. Soc. Am. 53, 5, 620, (May 1963).

  16. Product and Vacuum Technolgy Reference Book, (Product Catalog), Leybold Vacuum Products Inc.

  17. "Reflectance and Preparation of Front Surface Mirrors for Use at Various Angles of Incidence from Ultraviolet to the Far Infrared", G. Hass, J.B. Heaney, W.R. Hunter. Physics of Thin Films, vol. 12, pp. 1-51, Academic Press, NY, 1982.

  18. "Source Geometry Design Code and Coating Profile Measurements", B.A. Sabol, J.T. Williams. MMT Upgrade/Conversion Technical Memo #88-4, Oct. 1988.

View the corresponding figures

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6
Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12
Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18
Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24
Figure 25 Figure 26 Figure 27 Figure 28 Figure 29Figure 30
Figure 31 Figure 32 Figure 33 Figure 34 Figure 35 Figure 36
Figure 37