Thermal Coatings for In-vacuum Radiation Cooling LIGO-T070054-00-C R. Abbott, S. Waldman, Caltech 12 March, 2007 1. Overview and Background 1.1. There are instances in LIGO where the use of electronics packaging within the vacuum envelope is a necessity. This presents a unique thermal management challenge, especially where no direct conduction path exists. Barring conductive heat transfer, the only available method is by radiation cooling, where the radiation loss rate, P is described by the Stefan-Boltzmann Law: P= eσ A( T surf T amb ) 4 4 T surf is the temperature of the radiating surface, and T amb is the temperature of the surrounding environment - both temperatures are in degrees Kelvin. The area, A is in units of centimeterssquared (cm 2 ), the constant, σ is defined as ~5.67e10-12 watt/cm 2 K 4. The emissivity, e of a material is a measure of the ability to absorb or radiate energy. The value of e ranges over the theoretical limits of 0 to 1. A perfect radiator would be e = 1, whereas for all real-world materials, e is less than 1. 1.2. For a radiatively cooled design where temperatures and surface areas are fixed, the only method to achieve a higher rate of cooling is by increasing the value of the emissivity. A constraint on the upper temperature limit is set by the electronics housed in the pod. The upper limit for surface area is limited by an overall mass constraint. 1.3. There are many substances that can be applied to surfaces to increase its emissivity. An additional constraint for LIGO is that the materials must be compatible with stringent, ultra-high vacuum requirements. Ceramics, such as aluminum oxide or aluminum nitride, have high emissivities and can be applied to aluminum surfaces using a flame-spray process. The high temperatures associated with flame-sprayed ceramics (in excess of 5000 F.) are usually helpful for vacuum compatibility. LIGO has conducted measurements to measure the outgassing rate and species of commercially coated samples. 1.4. Literature suggests the following approximate values (and many others) for emissivities Table 1 Material Emissivity Aluminum: Strongly oxidized 0.25 Aluminum Oxide Flame-spray 0.765 coating 0.001 inch thick Aluminum Nitride ceramic 0.9 These numbers vary considerably depending on radiation wavelength, material finish and who s reporting, but the qualitative suggestion is that ceramic coatings offer promise of higher emissivities and warrant further examination. This paper assumes the solid angle effects of radiation-cooling are negligible. In practice, the solid angle effect is made negligible by ensuring the cooling surfaces have a clear line of sight to distant cool surfaces, most of which have good scattering properties due to their intrinsically rough surface finish.
2. Electronics Pod Description 2.1. Figure 1 shows an aluminum machined box with provisions for welded hermetic connectors. Boxes such as this are used to house in-vacuum electronics. Once the box is loaded with electronics, a tight fitting lid is laser welded in place. A specially designed port with a seal-screw (not shown) is built into the walls of the box. This permits a one-atmosphere helium-nitrogen backfill that is later used for leak checking. Once a satisfactory leak check has been made, the screw port is laser welded shut. For scale, the front face of the box measures 67mm by 39mm. Figure 1 3. Test Setup 3.1. The goal of the test was to measure the thermal properties of a standard object in vacuum using only radiation heat transfer. With this in mind, a test setup consisting of a vacuum tank, and a thermally non-conductive sample holder was constructed. Figure 2 shows the vacuum tank from Abbess Instruments, a Super-Bee convection gage from InstruTech Inc., and a Varian dry scroll vacuum pump. Figure 2
3.2. Figure 3 shows an aluminum nitride coated sample hanging from the swing-set used to isolate the sample from a direct conduction path to the vacuum chamber walls. A gold colored resistor used as a heater can be seen on the front face of the sample. A temperature sensor is tightly bonded to the rear of the sample. Tiny wires are used to minimize the longitudinal conduction of heat. Figure 3 3.3. Figure 4 shows a view looking into the top of the vacuum chamber. The black and white wires of the vacuum feed-through are visible at the top of the image. Also visible are black aluminum sheets that were added to the walls of the chamber. By conducting tests with and without the black sheets, it was possible to verify that the emissivity of the chamber walls was not a factor in the measurement. Figure 4
3.4. 6 identical bare aluminum plates were prepared. Two samples were left bare, two samples were coated with pure aluminum oxide, and the remaining two were coated with a 70/30% mixture of aluminum nitride /aluminum oxide. Figure 5 shows a coated aluminum oxide plate on the left and a bare reference plate. Figure 5 4. Test Process 4.1. The test consisted of putting a measured current into the resistive heater that was attached to the plate under test. The temperature of the plate and the temperature of the vacuum chamber walls were recorded during the test. The vacuum chamber was pumped down to a pressure of approximately 100mTorr during each test. All the data-runs were identical with the only variable being the coating on the sample. A reference run was conducted using a bare sample to establish a baseline. This baseline run was repeated with and without the black aluminum sheets lining the walls of the chamber. This was done to gain confidence that the emissivity of the chamber walls was not a significant factor in the results. 4.2. The heater was turned on in one step while data was taken. Once the samples reached thermal equilibrium, the Stefan-Boltzmann equation for radiation cooling could be used to calculate the average emissivity of the samples. Table 2 shows the physical details of the aluminum plates. Table 2 PLATE AREA CALCULATION Height Width Length Calculated Area in^2 Calculated Area cm^2 0.185 4.125 4.125 37.08 239.2 PLATE VOLUME CALCULATION DENSITY CALCULATION Calculated Volume in^3 Calculated Volume cm^3 3.15 51.6 Measured Mass Calculated Density (g) (kg/m^3) 138.25 2680.1
Test Results 4.3. The temperature plot of the temperature difference between the sample and the walls of a bare aluminum sample is shown in Figure 6. The step change in heater power is shown in green, and the delta in temperature is shown in blue. Input Power 0.98 watts Max. Temp rise ~30 deg. C Calculated emissivity ~0.23 Time to Equilibrium ~300min Figure 6 4.4. The temperature plot of the temperature difference between the sample and the walls of an aluminum oxide coated sample is shown in Figure 7. The step change in heater power is shown in green, and the delta in temperature is shown in blue. Input Power 0.98 watts Max. Temp rise ~7 deg. C Calculated emissivity ~0.96 Time to Equilibrium ~60min Figure 7
4.5. The temperature plot of the temperature difference between the sample and the walls of an aluminum nitride/aluminum oxide coated sample in a ratio of 70/30 is shown in Figure 8. The step change in heater power is shown in green, and the delta in temperature is shown in blue. Input Power 0.98 watts Max. Temp rise ~8 deg. C Calculated emissivity ~0.86 Time to Equilibrium ~75min Figure 8 5. Useful Tools No treatment on this topic would be complete without some practical tools to aid in the design process. What follows is a look at the underlying principles with an eye to being able to make useful performance predictions 5.1. Looking at the original Stefan-Boltzmann equation P= eσ A( T surf T amb ) 4 4 (Eq) 1 For the case of small temperature changes (few tens of degrees K about 290K) an approximation to (Eq) 1 is often sufficient. A 30K temperature rise above 290K yields an error of ~14% using the approximation (Eq) 2 vs. the exact solution (Eq) 1. For small changes in temperature, T a about an initial starting temperature, where the sample in question is essentially at equilibrium with the ambient environment, T o, the following approximation for the radiation heat loss, P out can be obtained by series expansion: P out =4eσ AT 3 o Ta (Eq) 2 This approximation represents the rate of radiation heat transfer from an object for a small change in that object s temperature, T a about a mean of T o. 5.2. The heat energy is introduced into this experiment by use of a resistive heater. Heat flows into the mass, m of the sample under test. Let c be the specific heat capacity of the sample. The equation for the rate of heat transfer into the sample, P in is:
P = cm (Eq) 3 in dta dt 5.3. By conservation of energy the equilibrium condition for the system is 5.4. Equating (Eq) 2 to (Eq) 3 yields: P in = P out (Eq) 4 dt dt cm a 3 = 4eσ AT T (Eq) 5 o a By rearranging dt dt 3 o 1 = 4eσ AT c m T (Eq) 6 a 1 a From the exponential solution to this differential equation, the reciprocal of the coefficient of T a, represents the time constant, τ of the system cm τ = (Eq) 7 3 4 e σ AT o From these expressions, it can be seen that increasing the sample emissivity, e, decreases the ultimate temperature of a radiatively cooled object, but also linearly reduces the time constant.
6. Vacuum Compatibility Results For those versed in reading such things, the test results from a residual gas analysis scan are included below. The main point of the vacuum test is that there is no significant outgassing detectable above background. Figure 9 shows a sample of clean bare aluminum. Figure 10 shows the aluminum nitride coated sample. Figure 11 shows the aluminum oxide coated sample. While the Y axis scaling has been mischievously tweaked, if you stare at the results long enough, you can reach the conclusion that the coated samples are essentially identical to the bare sample. This gives weight to the vacuum compatibility of the coatings and the coating process. Figure 9
Figure 10 Figure 11