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by: Malvina Orn


Malvina Orn
GPA 3.77


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This 10 page Class Notes was uploaded by Malvina Orn on Monday September 7, 2015. The Class Notes belongs to PHY 386K at University of Texas at Austin taught by Staff in Fall. Since its upload, it has received 74 views. For similar materials see /class/181837/phy-386k-university-of-texas-at-austin in Physics 2 at University of Texas at Austin.




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Date Created: 09/07/15
Pressure torr 10 11 10 9 10 7 10 5 10 3 10 1 101 103 Figure 1 Gauges used in various pressure ranges 1 Pressure Many modern physics experiments are carried out in a reduced pressure environment usually to isolate a sample of interest from outside in uences For example a metal surface might become covered with molecules adsorbed from the gas phase or the particle beam in an accelerator might be attenuated by collisions with background gas in the beam pipe the solution is to pump away the gas This section deals with techniques used to measure pressure from atmospheric pressure down to the lowest pressures that can be produced in a laboratory a range of roughly fteen orders of magnitude Figure 1 shows approximate ranges for a selection of commonly used pressure gauges Two of the gauges shown in gure 1 measure pressure directly the rest use a secondary physical process to measure something that is related to the pressure The direct gauges are the mercury manometer shown in the gure to the right and the capacitance manometer shown in gure 3 In a mercury manometer gas is allowed in to one arm of a U shaped tube lled with liquid mercury The other arm is evacuated Re ection of the gas molecules at the mercury surface involves momentum exchange and this results in a pressure The height differ ence between the two arms is a direct measure of the pressure difference and is given in mmHg or Torri Atmospheric pressure will support a column of mercury 760 mm high Such an apparatus is bulky and can be messyi 1n Otto Sternls laboratory in Hamburg in the 1930 s mercury manometers were used as detectors in atomic and molecular beam scattering experiments A gure from one of Stern7s papers is shown in gure 2 Through a combination of clever compensation and careful circuit construction it seems that Stern and zum Naif zun MmpElsa L NunsHangmast ZU lm t Fig 7 Neue marlinmg Figure 2 Early beamrsurface scattering from Estermann and Stem zs f Phys 61 95 1930 coworkers were able to measure pressure di erences at the astonishing level of 1078 mmHg This is roug the thickness of one atomic layer of Hg Damn those guys were good The apparatus shown in gur as used to observe the di raction of helium from a crystalline LlF surface and was the demonstration of the de Broglie w beginnin hly e 2 rst experimental ave character of something heavier than an electron This marked the of the eld of atom optics A second type of absolute pressure gauge is the capacitance manometer shown schematically in gure 3 It consists of two parallel discs one xed and one exlb e that form the plate is gas permeable and t e exlble one is not A pressu gure of a capacitor The xed disc e difference between the two sides ref and Sig in the will cause the exible membrane to bow and the capacitance to chan e Capacitance manometers can be very accurate but are fairly expensive A typical pressure head covers 5 orders ofmagnitude and can be purchased with di erent disc thicknesses for di erent ranges a circular membrane clamped around the rim the displacement from atness as a function of radial position r and pressure P is given by Pa 7 2 W T m 1 3 EhS 121 7 Where the Variables are 39 39 quot h 39 39 quot 39 with D a E is 1 is Poisson s ratio The material properties appearing in this equation are well measured and the rest of the te s are geometry Thus w d i j m n b l i t i Pb Potential problems Fixed Electrodes l Diaphragm Figure 3 Schematic of a capacitance manometer headi include measurements involving condensible gasses eigi water which can have a big effect because of its large dielectric constant and mechanical resonances think of the exible membrane as a drum head The resonant frequency is give by 1 s pg where s is the radial tension force per unit length on the disc A modern day version of a diaphragm pressure gauge is shown in gure 4 Here a deep depression is fabricated in a single crystal silicon wafer and a second flat piece of silicon is bonded over it A hole in the bottom piece lets in gas e top piece has two pizeoresistors fabricated on in by ion implantation since silicon is not a piezoelectric material The resistance of these is dependent on the stress in the material One the these resistors R2 the reference is placed over the thick supporting material and the other R1 is placed over the thin membrane If the pressure difference across the thin membrane is different from zero the membrane will distort and the resistance of R1 will change A second structure used as a reference is fabricated on the same silicon wafer but not connected to any gas sample The resistors are connected to form a Wheatstone bridge with ampli cation also built into the chip Such devices are in widespread use in air conditioning systems and in automobiles and can be purchased for a few dollars or less A similar pressure gauge in which the inductance is measured instead of the capacitance is shown in gure 5 The dark areas between the horizontal bars of the E represent a coil of wire with the windings coming out of and going into the page The magnetic eld lines then circulate in the plane of the page Most of the path for the eld lines is within the gray area of the gure which is a material with high magnetic permeability However there is a small air gap this gap is effectively a volume with a high magnetic resistance that is the inductance is dominated by the spacing of the gap When the pressure is changed the thin plate on the right deforms and the inductance of a circuit containing the element changes This change is calibrated to the pressure Usually two of the E structures are sandwiched together and one is used as a reference This is shown in gure 6 The spinning rotor gauge sometimes called a viscosity gauge is shown in gure 7 Several sets of electromagnets are used to rotate a magnetic ball usually at 400 Hz a secondary standard for transformers Another set of magnetic coils is used to monitor the rotation The ball is spun and then allowed to drift for a period of time and the decay of the rotation is monitored Collisions with gas molecules slow the rotation rate during the drift timer The rate of change of the rotation frequency is given by a 10 1 p w 7 7r ad 6 where a is ball radius d the ball density p is the gas pressure and E is the average gas speed This expression is based on two assumptions One the angular distribution of the molecules leaving the surface of the rotor is symmetric about the surface normal an assumption that appears to be quite well obeyed for R1 R2 Diaphragm Reference pressure Figure 4 Schematic of piezoresistors on a silicon diaphragmi A E Figure 5 Variable reluctance pressure sensor A basic principle of operation B an equivalent circuit From reference i ss nmmusu PRESSURE PRESSURE FURY cm39nEs Figure 6 Construction of a VPR sensor for low pressure measurements A assembly of the sensor B double E core at both sides of the cavity From reference 1 i a real microscopically rough adsorbate covered surface The second assumption is that the gas is in the free molecular ow regime that is that a gas molecule travels from the walls to the rotor without colliding with other gas molecules Note that the expression given above involves no calibration as all the pressure gauges discussed in what follows so the SRG is arguably an absolute gaugei In addition it is linear in the pressure It is used in the range from about 10 2 down to 10 7 torri At higher pressures the gauge becomes nonlinear because of collective motion in the gas owi A thermal conductivity or thermocouple gauge illustrated at the right uses heat transport to measure gas pressure A thermocouple is placed near a heated lament and then one of two things is measured 1 the temperature of the thermocouple is measured for xed power dissipation in the lament or 2 the lament power required to maintain a constant thermocouple voltagei Energy transfer from such a heated lament versus the gas pressure is plotted in gure 8 an equivalent and more insightful scale for the xaxis in this gure is the Knudsen number which is the ratio of the mean free path to some relevant apparatus dimensioni Three regimes are readily identi ed in the gure which demarcate the useful pressure range of a thermocouple gaugei At low pressure energy transfer is all radiative and the gauge is insensitive to the gas pressure At intermediate pressure heat transfer is conductivei The gas is in free molecular ow collisions are with the surfaces of the lament and thermocouple and gas phase collisions are negligible This is the linear central portion of the graph At higher pressures heat transfer is by convection and gas phase collisions become important In this range the heat transfer still varies with gas pressure but at a much slower rate and it becomes very dependent on the gas species This latter effect is shown in gure 9 A recent improvement on the thermocouple gauge is called the convectron gaugei According to the manufacturer it uses a large gauge volume to enhance convective energy transfer and can be used up higher pressures even up to atmospheric pressure although the dependence of the response becomes extreme However these gauges are very robust and have become the instrument of choice for use on forelines in high vacuum systems A breakthrough of sorts occurred in the 1950s with the invention of the hot lament ionization gaugei This allowed the lowest pressure that could be measured to be extended into the 10 8 torr range and with future enhancements into down to 10 11 torri The layout of the BayardAlpert the inventors gauge is shown in gure 10 A lament tungsten or Figure 7 Spinning rotor guage R e rotor V e vacuum enclosure partially cut away for illustration M 7 one of two permanent magnets A 7 one of two pickup coils for control of axial rotor position L 7 one of four coils for lateral damping D 7 one of four drive coils P 7 one of two pickup coils From 1 K nemerey JVST A 317151985 Pressure mTorr Heat Transfer Knudsen Number id Figure 8 Heat transfer regimes typical of a thermal conductivity gauge PRESSURE Ton 04 06 v x 2 39 2 He 140 N2 02 I0 A I20 AIR 0 CL w 05 g loo FREON 22 E a r 3 so 06 E H20 g J In 5 so H E 3 04 lt 40 quot9 02 02 zo 0N22 AIR n I00 I20 I40 40 so IMJICATED PRESSURE Po Figure 9 Calibration curves for a thermocouple gauge tuber tungsten doped with thorium is heated sufficiently hot 17001800 K to generate electrons by thermionic emission The electrons are accelerated by a potential difference of 100 volts typical toward a grid grid is biased at 180 V with respect to ground Inside the grid ions are produced by collisions e A A 26 Ai In the center of the grid is a bare metal wire the collector connected to ground via a sensitive current meteri An ion is therefore attracted to the collector When a positive ion nears a metal surface it is neutralized with essentially unity probability The electron required to do this neutralization is measured y the ammeterl Both the rate of ionization and the conversion of ions to electrons at the collector are linear in the pressure for pressures below about 10 4 torrl For pressures above this a collisional cascade starts to occur The lament in the ion gauge is biased about 80 volts with respect to ground so that the thermally emitted electrons go to the grid and nowhere else such as the chamber wallsl These electrons oscillate multiple times in the potential well produced by the grid before eventually being neutralizedi The current between the lament and grid is measured as a feedback signal to control the lament heating power It is also used to detect an overpressure condition where the lament is hot but no electrons are reaching the grid in this case the lament is shot off to prevent burnouti The lower limit on the pressure that can be measured by an ionization gauge is called the X ray limit and results from the following process Electrons that hit the grid have suf cient kinetic energy to cause photon emission a process called inverse photoemissionl The tail of the energy of these photons extends into the UV and Xray region of the spectruml A small fraction of these higher energy photons hit the collector and cause photoemissionl The electrons head straight for the grid but the loss of electrons at the collector looks just like ion neutralization and leads to a background current in the ammeterl For a grid constructed of ne wire this dark current corresponds to a pressure of about SXlO 11 torr the Xray limiti To measure lower pressures requires a mass spectrometer which is the subject of section 2 The ionization probability depends on the both the gas identity and the electron energy The dependence on gas species is shown in table 1 and essentially tracks the ionization potential of the atom or molecule Thus the gauge is less sensitive to hydrogen and helium and more sensitive to C02 and kryptoni An ion gauge built to standard specifications commonly has a sensitivity 8 of lOtorri The collector current is then i sieP where i8 is the emission current and is typically 10 milliampsi This puts i in the range of nanoamps which is easily measured For reactive species the ions are actually implanted in the collector so the gauge functions as a kind of pump not too different than an ion pump albeit with a low pumping speed of a fraction of a liter per secon i The hot lament in a BayardAlpert ionization gauge can result in contamination when used to measure Table 1 Experimental Total Ionization Cross Sections at 70 eV Electron Energy Normalized to Nitrogen Gas Relative Cross Section H2 042 He 0 14 CH4 157 Ne 02 N2 100 CO 107 C2H4 244 NO 125 02 1 02 Ar 119 C02 136 N20 148 Kr 1 81 Xe 220 SFB 242 Figure 10 Schematic circuit for a BayardAlpert ionization gauge the pressure of more reactive gases as they can be decomposed on the lament An alternative is the cold cathode or Penning gauge shown schematically in gure 11 Here a high voltage difference is applied between two electrodes and electrons can escape the negative terminal A magnetic eld along the axis of the device causes the electrons to travel along a spiral path where they can cause collisional ionization of the background gas The ions don7t curve as much in the magnetic eld and travel to the negative electrode where they are neutralized and measured These devices tend to be very robust particularly against sudden pressure bursts7 not having any hot lamenti a B coils Figure 11 Schematic of a cold cathode ionization gaugei References 1 Jacob Fraden Handbook of Modern Sensors77 Springer Verlag New York 1996 Appendix Reference Results from the Kinetic Theory of Gases MaxwellBoltzmann speed distribution m 32 772152 2 4N 4 271le W C 4 Where c is the speed m is the mass T is the temperature in Kelvin and k is Boltzmannls constant k 1381x10 23 JK 8631x10 5 eVKi The average speed is The mean free path is 1 A wde Where p is the density and d is the effective particle diameter7 typically around 013 nmi The rate of collisions With a surface is 1 Zwall 165 For an ideal gas7 the average kinetic energy is 3 E kT k 2 Pressure and kinetic energy are related according to At room temperature kT 25 meVi Conversion factors 1 Pa 145x10 4 lbin2 9869x10 6 atm 71quot 10 3 mm Hg Flux near centerline from an effusive beam 7 EASAC 7 P 5 c 7 4 7rd 27ngkBTg12 d3 Beam intensity at a target p5 A5 7 P s 4 7rd ZNMngTg12 d B Table 2 Typical numbers for N2 at 298 K E 475 ms7 d01316 nm Pressure Density cm g Mean Free Path Zwall cm 2 s 1 ML time 10 6 torr 324x1010 6916 m 385x1014 0385 s 10 3 torr 324x1013 6916 mm 385x1017 0385 ms 1 torr 324x1016 696 Mm 385x1020 0385 Ms 1000 torr 324x10lg 6916 nm 385x1023 0385 ns


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