Pressure 1 torr 1 mbar 100 Pa

Gas Kinetic Theory:

Bulk Behavior vs. Molecular behavior

Mean-Free Path ( ) size of container: fluid, viscous flow; flow rate responds to pressure as molecules interact. Geometry of walls can affect flow of gas. size of container: billiard table. Interactions with walls dominates, molecular flow; gas flow is statistical, from high P because of diffusion.

5-500 mtorr is transition between above.

Gas Flow:

Pumping speed is defined as the time rate of change of the Volume:

Similarly, the capacity of vacuum specified by the inlet pumping speed:

We now wish to relate the pumping speed, S, to the mass flow rate of a gas system. To do this, we take the time derivative of the Ideal Gas Law with time-constant pressure and temperature:

Or putting in the mass in the RHS of the equation and substituting

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Vacuum LectureTuesday, July 8, 2014 1:07 PM

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Or putting in the mass in the RHS of the equation and substituting

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Solving for the mass flow rate, we have

Therefore, the mass flow rate is proportional to the throughput, , defined as

The units of the throughput are

. Throughput is often measured in or standard cubic

centimeter per minute, which is at and .We now derive a second equation to complement Eq. 1 above; we would like to express in terms of the conductance. We find (see hand-written notes)

where is the conductance of the channel, , and we are referring to the following picture of the vacuum system:

Eq. 2 is equivalent to Ohm's law

. So conductances add in series and parallel in the following

network equations:

Speed at pump inlet is

We now derive the master equation.

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Speed at pump inlet is

The throughput is

Then the master equation is:

If C is too small, then S will be too small because Sp is fixed. Rule of thumb: C = 4 S so Sp is close to the desired S.

In the hand-written notes we derive the conductance formulae for dense fluids. For gases in viscous flow regime (pressure driven), with a circular pipe of diameter D, length L, and viscosity and average Pressure and at room temperature we find

measured in , and where is measured in and lengths are in . Note that it depends on the average pressure, in contrast to our derivation of the conductance for a dense fluid like water.

In the molecular-flow region (diffusion driven)(N.B. No pressure dependence) at room temperature for air:

Measured in L/s.

Example of bad design: 100 L/s diff pump with 2.3 cm diameter tube 10 cm long,

Also, constant throughput means:

So it is important to place gauge in right location. At mouth of pump would be 6 times lower than at locations of P1.

Pump down time:•

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Rate of gas evolution depends on nature of solid and adsorbate. Typically exponential decay in time.

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Water and carbon dioxide from the air are adsorbed most tenaciously. ○

A rough, porous, or polar surface adsorbs more gas than a clean polished surface.○

Baking 150-200 deg C helps.○

Following exposure to air, stainless steel outgases at roughly 10-8torr L/s/cm2 of surface area after an hour of pumping at room temperature. A day of pumping may be required to reduce this rate below 10-9torr L/s/cm2.

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Al is 10 X worse,○

Plastic is 100X worse.○

Rubber is 1000X worse still.○

Outgassing.:•

In low-pressure regime, off-gassing and desorption may contribute to gas load and will alter this. Derive this in class, it uses definition of pumping speed and ideal gas law at constant V and T.

Example: Maintain 10-7, with 10-9torr L/s/cm2 outgassing rate. This requires 10-2 L/s for every cm2 of area. A 1 m diameter and 1 m high bell chamber needs a 400 L/s pump with a 10 cm inlet port. Getting to 10-8 would be nearly impossible.

Pressure and Flow Measurement:

The pressure within a vacuum system may vary over more than 13 orders of magnitude. No one gauge will operate over this range, so most systems are equipped with several different gauges.

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Hydrostatic Gauges (0.1 -1 torr): oil, mercury manometers.○

Mechanical Gauges•

A McLeod gauge is a type of Hydrostatic gauge capable of 100 .

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Mechanical: A number of different gauges depend upon the flexure of a metal tube or diaphragm as

a measure of pressure. In the Bourdon gauge, a thin-wall, curved tube, closed at one end, is attached to the vacuum system. Pressure changes cause a change in curvature of the tube.

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Piezoelectric Pressure Transducers. A piezo transducer is an absolute, direct-reading device that senses the gas pressure on a piezoelectric crystal. They function in the 10-1 to 1000 torr range. Good for roughing and forline pressures.

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Capacitance Manometers. A capacitance manometer is a diaphragm manometer wherein the

position of the diaphragm is determined from a measurement of electrical capacitance. Capacitance manometers are available to measure pres- sures from 1000 torr down to less than 10-4torr. Also have 10 ms response so good for pressure feedback!

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In both gauges a wire filament is heated by the passage of an electrical current. The temper- ature of the filament depends on the rate of heat loss to the surrounding gas. Thermocouple uses a thermcouple and Pirani uses a Wheatstone bridge. Normally calibrated for air.

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Thermal-conductivity Gauges: The thermal conductivity of a gas decreases from some constant value above about 10 torr to essentially zero at about 10-3torr. This change in thermal conductivity is used as an indication of pressure in the Pirani gauge and the thermocouple gauge. They are low-cost and rugged and easy to use.

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Spinning-rotor gauges are an example and provide absolute pressure measurement between

and torr with an accuracy of a few %. The use a spinning levitating steel ball and "ring-down" times to meausure viscosity. Expensive.

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Viscous-Drag Gauge: uses pressure dependent viscosity in molecular flow regime.•

Ionization Gauges. In the region of molecular flow, in this type of gauge, gas molecules are ionized by electron impact and the resulting positive ions are collected at a negatively biased electrode. The current to this electrode is a function of pressure:

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Hot cathode ionization gauge, electrons are produced by thermionic emission from an electrically heated wire filament.

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Cold cathode gauges, electrons and ions are produced in a discharge initiated by a high-voltage electrical discharge

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this electrode is a function of pressure:

A hot cathode ionization gauge (Bayard-Alpert) in both above:○

Electrons from an electrically heated filament (F) are accelerated through the gas toward a positively biased, helical wire grid (G). Collisions between the accelerated electrons and gas molecules create ions that are collected at a central wire electrode (C), and the positive ion current is measured by a sensitive electrometer. These gauges are useful in the 10-3 to 10-10torr range (the filament burns out above 10-3 torr).

Ion current is proportional to pressure (make sense intuitively). Sensitivity factors for other gases are shown, since these are normally calibrated for air.

Ion gauges can cause local lower pressures because of ionization and metal evaporation from the filament creates nice clean surface for gettering. This may lead to errors in pressure readings. Circumvented by using "nude" gauges.

They can be degassed by heating the grid coil to incandescence. Degas for a few minutes at 10-4, then again every 10-2 drop.

Come in two flavors: tungsten (more stable but doesn't like hydrocarbons) or thoria-coated iridium.

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Cold cathode gauges include Penning gauges, magnetrons, inverted magnetrons, and Philips gauges. They use ~ kV potentials on two electrodes to measure pressure. Currents are high. They are inexpensive and robust and operate from 10-2 to 10-7.

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Mass spectrometers. Determine partial pressures of gaseous chemical species and detect leaks. Residual Gas Analyzers (RGAs) are cheap mass specs sensitive to masses 2-100 amu. They operate from 10-5-10-14 torr. Leak detection is done by monitoring Helium and spraying outside of chamber with He.

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Differential pressure flowmeters; measure pressure at each end of a tube of know conductance in viscous or molecular regime.

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Flowmeters.•

Thermal Mass Flowmeter; viscous flow regime where thermal conductivity is constant. Temperature profile of tube is measured as gas flows through and is used to measure flow rate. Calibrated in standard cubic centimeters per minute or SCCM. SCC is gas contained in one cubit cm at 1 atm at 0 deg. C. Usually calibrated for air or nitrogen with a correction factor for other gases. 1-10^5 sccm with 1% accuracy.

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Vacuum Pumps:

All have certain pressure ranges. In general, viscous flow and molecular flow pumps are incompatible with the other regime, so pumps must be used in series. Also, some pump certain gas species better than others, so pumps are also used in parallel.

Capacity 1-500 L/m, single-stage down to 50 mtorr.

Oil-sealed rotary vane pumps: rotor turns off-center within a cylindrical stator, spring loaded vanes separate two volumes. Air is compressed and forced through a one-way valve sealed with oil. Oil has very low vapor pressure. Best to keep running, can run for years. If base pressure goes up, oil has been contaminated; drain, fill, run, drain, and fill again. When storing, fill with new oil and seal ports.

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Mechanical pumps go as low as 5mtorr to 5 torr. Good for maintaining other pumps below critical backing pressure, so sometimes called backing pumps or foreline pumps or forepumps. Also called a roughing pump, used to get other pumps into operational mode.

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Roots Blower: displacement pump with no oil (dry). lobed rotors compress gas. Down to 10-3 torr and up to several 1000 L/s.

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Piston pumps: teflon pistons are dry and good for no hydrocarbon backing down to 50 mtorr.

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Diaphragm pumps: clean, poor throughput.○

Molecular Drag Pumps: Uses fast rotating concentric cylinder with helical grooves. Air is grabbed or redirected by rotor and exhausted. Very high compression at exhaust requires backing pump. Also will not operate until inlet is 1 torr, so additional pumps are needed. Virtues are 30L/s throughput in 1mtorr to 1 torr range, so good for short pumping times.

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Turbomolecular pumps: molecular flow regime, uses stacks of canted jet turbine engine

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Achieve 10-1000 L/s and 10-10 torr is possible.

Bearings are key, some are water cooled and now can even be magnetically levitated.

Turbomolecular pumps: molecular flow regime, uses stacks of canted jet turbine engine spinning up to 90k rpm and oppositely canted, interleaved stators to compress gas toward exhaust. Has compression ratio that varies with molecular weight, higher for heavier, so turbos can make very oil free chambers; not so good with light gasses like H or He. Only as good as backing pump: compression goes down by 10^7 from 0.1 to 1 torr at exhaust!

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Can be combined with Molecular drag pump to for hybrid that only requires 1-10 torr backing.

Now made with dry diaphram and everything together (turnkey):

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Support by inlet flange, never by body; forces or torques should never be applied to body.

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Use a protective screen (splinter shield) to avoid having larger particles hit the rotors.

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Vent slowly to avoid damage of rotors.□If using oil backing, turbo on must be timed to avoid oil back-streaming. Once at 50% speed, oil is easily kept out. During venting, valve must shut between oil backing and turbo, and the turbo vented at 50% to avoid oil back-streaming from bearings.

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Keep an unused turbo on.□

Concerns with Turbos:

Working fluid (oil or Hg) is vaporized and ejected from nozzles in a spray toward cooled walls that condense fluid on impact. Walls have T gradient (lower T upper), the higher T lower allows gas to evolve.

Good for light gasses because of momentum transfer (oil hits molecule to the wall).

4 L/s per cm2.

If they evacuate at too high pressure, mean-free-path is to short and molecules get redirected away from wall and pumping speed is reduced (see graph)

Need 500 mtorr backing or they stall, and oil streams up into the vacuum chamber. Cooling caps and cold traps are used to avoid oil vapor backstreaming.

Lowest pressure determined by vapor pressure of working fluid.

No moving parts = long lived.

High throughput: 50-50000 L/s are possible.

Economical for large vacuum chambers.

Vapor diffusion Pumps:○

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Here is a LN2 baffle:

Sorption pumps: use molecular sieves such as activated charcoal or zeolite. Huge surface area 1000s m2 per gram.

Cooled to LN2 to remove air.

Activated by baking @ 250 deg C.

Can reach 10-2 torr in 20 minute for 100 L chamber.

Can reach microtorr if three are used sequentially.

No good for H and He.

Entrainment Pumps: chemical or physical trapping to solid; contain no fluids that can contaminate.

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Pumps O2, H2, H20, etc. at ~ L/s per cm2 of surface at room temp.

No good for methane and noble gases (He, Ar, etc)

Can operate between 10-3 to 10-11 torr, but metal must be continuously evaporated for pumping to work well. Here are a few ways to do it.

Getter Pumps: clean surface of refractory metals: titanium, molybdenum, tantalum, or zirconium will pump most gasses by chemisorption, in a process called gettering.

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Cryopumps: relies primarily upon condensation on a cold surface; cools surface to 10-50 K and allow gases to condense. Needs mtorr before turning on.

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10-3 to 10-11 torr, 1-1000 L/s.

Lifetime shortened with more pressure. 100 hours at 10-3, 6 years at microtorr, forever at nanotorr.

Very clean, no moving parts.

Can be expensive.

Ion pumps: 5-10 kV applied between Stainless anode and Ti cathode, this makes air plasma which accelerates toward Ti cathode burying the ion and sputtering Ti which can then getter as well. Current is measure of pressure.

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Vacuum Hardware:

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He diffuses quickly through Quartz

High T 1000 deg C.

Glass: borosilicate (Pyrex and Kimax) 70% SiO2 and also pure Quartz○

Ceramics: electrical insulators and thermal isolators, not very easily machined; MACOR is machinable ceramic.

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Brass and copper; brass has zinc which is volatile below 10-6 torr.○

Stainless Steel: American AISI type 304 and 316 are used; 303 not used because of volatile components added to improve machinability.

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Aluminum: 6000 series alloys are used down to 10-7 torr, very light and strong but porous so outgassing 10X greater than stainless. Oxide also a problem with electrostatic build up.

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Polyamide/imide, PTFE; kapton is polyimide sheet.

Greases like apiezon M for vacuum applications to 10-8 torr.

Plastics: outgas air, water, plasticizers, etc. Only used down to 10-7 torr, cannot be heated.○

Materials (see outgassing data here http://outgassing.nasa.gov/):•

Pipe threads: use teflon tape○

ASA flanges (old): two flat flanges with recess for O-ring□QF (quick flange) of KF (klein flange): two flat flanges with recess for O-ring with center ring to keep gasket from going inward. Use circular clamps with thumbscrew. Come from 10-50 mm.

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O-ring sealed flanges and "quick disconnect"

O-rings: down to 10-7 torr, Buna-N and Viton-A (fluorocarbon polymer) is best because higher T and lower outgassing. In general, outgassing limits them.

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Demountable Vacuum Connections: vacuum tight seals between mating connectors formed by pipe thread with joint sealant, elastomeric O-ring gaskets, or deformable metal gaskets.

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ISO flange; larger than KF 63-630 mm, but still use elastomeric O-ring□

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Static O-rings should be cleaned with lint free cloth and used dry, never clean with solvent.

Rotating O-ring seals can use small amount of vacuum grease.

Hand tighten□1/2 turn per bolt until flange faces just touch.□

ConFlat or CF flanges have two flat flanges with knife-edge ridges cut into a OHFC (oxygen-free high thermal conductivity Copper) copper gasket when drawn together with bolts. Can be baked to 450 C. Care must be taken when tightening:

Metal Gaskets flanges:○

Valves…things to consider in order of importance:•(i) conductance(ii) operating temperature(iii) leak rate around the valve-operating mechanism and the valve seat;(iv) material of construction [related to (ii)](iv) configuration(v) cost(vi) reliability

Glass valves: stopcock and Teflon plug○

(vii) ease of maintenance.

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Piston-type: poor conductance; two right-angles

Buttefly: excellent conductance

Sliding-gate; excellent conductance

Metal Valves: differ by how plate seals with valve seat. Lower quality vacuum valves use viton O-ring as opposed to metal. Rotating handwheel or crank actuation are most robust.

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Mechanical Motion:•

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Sieves○

Traps and Baffles: Foreline traps (between rough pump if oil is used and better vacuum pump, like turbo)

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Thimble traps and baffles.○

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At 10-4 torr, breakdown V is 1000 V. Sharp points will break down at lower V, but melt and smooth.

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All wires at different V must be insulated from each other. Insulation materials that are clean and that do not outgas are a must.

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Alumina is good. Even make Alumina circuit board○

Can laser cut Alumina.○

Alumina is porous so use gloves.○

Teflon insulated wire is also good down to 10-7 torr.○

Kapton (polyimide) coated wire is available for use down to UHV (<10-8 torr); Kapton tape is great for holding things down. See http://outgassing.nasa.gov/.

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Soldering with lead-based solder and flux is bad. Silver, indium-based solder is good.○

Electronics and electricity in Vacuo:•

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Alumina printed circuit board for vacuum work.

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