Diploma thesis in Physics submitted by Florian Freundt born in ...

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4.1. Mass spectrometry of He, Ne, Ar, Kr and Xe 4 Measuring methods to their respective desorption temperatures. Depending on the gas amounts present within a sample, a splitting step is required and was initiated if a specified limit was exceeded. This was determined after separation using a quadrupole mass spectrometer to estimate the abundances of each noble gas. The gases were detected using a Faraday cup ( 4 He, 20 Ne, 22 Ne, 36 Ar, 40 Ar) and an electron multiplier ( 3 He, 84 Kr, 132 Xe). A specified volume of gas (atmospheric air of known noble gas composition) was measured at least once a day as a calibration standard and to characterize the long term stability of the measurement process, short term variations were characterized by fast calibrations executed before every sample measurement, using pure He, Ne and Kr-Xe gases. 4.1.2 Determination of sample gas amount The amount of gas inside a sample tube was calculated using two different methods, both based on the ideal gas law but relying on independently measured parameters. The first method utilizes the empirical formula A.6 created by Wieser [2006] that relates the sample tube length (at its closed state with squeezed ends) to its volume. The inline pressure during sample shutoff and ambient temperature were measured during sampling. This method isn’t very accurate though since both volume calculation and temperature measurement are prone to large errors, resulting in relative errors in gas amount of 2.5 – 4.5 %. Details of the calculation can be found in equation A.5. The second method uses the gas pressure inside the inlet volume pinlet of the mass spectrometer, as well as the laboratory temperature TLab after expanding the gas sample into the evacuated inlet volume. The inlet pressure was measured using a Keller Lex 1 pressure gauge with a nominal accuracy of 0.5 mbar (Datasheet D.3). The inlet volume was calculated from volumetric measurements, by expanding air at known pressure from a known volume of a different part of the mass spectrometer preparation line into the inlet volume. Details of the inlet volume calculation can be found in Appendix A.2. Since the most important parameters of this method were measured with better precision and accuracy than those of the the other method, the accuracy of the calculated gas amount was superior. Average relative errors achieved by this gas amount measurement are at 1 %. Therefore this method, utilizing the inlet pressure, was chosen over the other for all further calculations and data evaluations. The equation (detailed in Appendix A.1.2) derived from the ideal gas law includes a correction for the sample tube volume derived from its mass mCu and density ρCu as well as a correction for the water vapor pressure pH2O due to humidity within the sample gas: � (pinlet − pH2O) · VC − n = mCu � ρCu TLab · R The vapor pressure of water pH2O is part of the total pressure in the sample tube and therefore must be included in the calculation of the gas sample size. Neither water vapor pressure nor the relative humidity were measured directly during or after sampling. Instead it was assumed 44 (4.1)
4 Measuring methods 4.1. Mass spectrometry of He, Ne, Ar, Kr and Xe that the relative humidity of soil air is always higher than 95 % in non-arid regions [Hillel, 1980]. The vapor pressure of water was thus calculated from this assumption of relative humidity, as detailed in Appendix A.1.1. 4.1.3 Estimation of relative humidity within the inlet section Expanding the gas sample into the inlet volume of the mass spectrometer results in a change of its relative humidity φ due to the increase in volume, φinlet �= φsample. Therefore the calculation of the water vapor pressure has to be based on this new relative humidity φinlet, which is calculated from the actual mass of the water mW,sample contained in a sample tube using the absolute humidity ρW: ρW = mW,sample Vsample and ρW = φsample · ρW,max(T ) (4.2) ⇒ mW,sample = φsample · ρW,max(T ) · Vsample (4.3) The maximum vapor pressure above water ρW,max(T ) at a given temperature T is calculated using the Magnus Formula [WMO, 2008] ρW,max(T ) = EW(t) RW · T EW(t) = 6.112 hPa · exp � 17.62 · t 243.12 ◦C + t � with the water vapor content EW(t), the specific gas constant of water RW = 461.52 J kg K and the temperature T [K], t [ ◦ C]. Assuming φsample ≈ 100 % for soil air [Hillel, 1980] leads to mW,sample = EW(t) RW · T · Vsample (4.6) The sample volume is calculated using formula A.6, the sampling temperature however is of very low accuracy. Soil air temperatures were not measured in situ during sampling at the respective sampling depths. In addition, the sample gas temperature was influenced during sampling by the process of pumping the soil air from the ground and through a copper tube at ambient atmospheric temperature as well as by changing conditions (wind, direct sunlight versus cloud cover) during sampling. Therefore the relative error of sampling temperature measurements is estimated to be 5 %. The relative humidity within the mass spectrometer inlet volume is given by φinlet = mW,sample Vinlet · ρW,max(TLab) where TLab is the average temperature of 24 ◦ C within the laboratory, and Vinlet = (26.832 ± 0.252) ml for runs 1 – 3 and Vinlet = (27.212 ± 0.153) ml for run 4, see Tables B.4 and B.5 for the resulting relative humidities. 45 (4.4) (4.5) (4.7)
Page 1: Faculty of Physics and Astronomy He
Page 5: Measuring annual variation of soil
Page 8 and 9: CONTENTS CONTENTS 3.1 Setup of the
Page 11 and 12: Chapter 1 Introduction Understandin
Page 13: 1 Introduction Molins and Mayer [20
Page 16 and 17: 2.1. Noble gas temperatures 2 Theor
Page 24 and 25: 2.2. Physical processes and propert
Page 26 and 27: 2.2. Physical processes and propert
Page 28 and 29: 2.3. Soil atmosphere composition 2
Page 35 and 36: Chapter 3 Sampling sites and method
Page 37 and 38: 3 Sampling sites and methods 3.1. S
Page 43: Chapter 4 Measuring methods 4.1 Mas
Page 47: 4 Measuring methods 4.2. On site me
Page 50 and 51: 5.2. Temperature profiles 5 Results
Page 52 and 53: 5.3. O2 and CO2 profiles 5 Results
Page 54 and 55: 5.4. Borehole sealing 5 Results 5.4
Page 56 and 57: 5.4. Borehole sealing 5 Results Fig
Page 58 and 59: 5.5. Noble gases 5 Results 8 days,
Page 60 and 61: 5.5. Noble gases 5 Results 5.5.3 So
Page 62 and 63: 5.5. Noble gases 5 Results 5.5.4 So
Page 64 and 65: 6 Discussion This rather extreme am
Page 66 and 67: )! )! *+,-./-01234*-56-20301.7*38*9
Page 68 and 69: 6 Discussion Table 6.1: Synthetic d
Page 71: Chapter 7 Summary The results of th
Page 74 and 75: 8 Outlook Considering the manifold
Page 76 and 77: A.1. Gas sample size A Calculations
Page 78 and 79: A.3. Fractionation-Values A Calcula
Page 80 and 81: Table B.3: Noble gas volume mixing
Page 82 and 83: Table B.5: Calculated values of rel
Page 84 and 85: Table B.8: Precipitation record of
Page 86 and 87: Table B.10: Complete dataset of nob
Page 89 and 90: Appendix C Additional plots and fig
Page 91 and 92: C Additional plots and figures Figu
Page 93 and 94: C Additional plots and figures �
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C Additional plots and figures Figu
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C Additional plots and figures O 2
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C Additional plots and figures 4 He
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C Additional plots and figures 20 N
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C Additional plots and figures Figu
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C Additional plots and figures 10 1
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Appendix D Datasheets 107
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D Datasheets LogTag TREX-8 Technica
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Bibliography [Aeschbach-Hertig 1994
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BIBLIOGRAPHY BIBLIOGRAPHY [Friedric
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BIBLIOGRAPHY BIBLIOGRAPHY [Riveros-
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Acknowledegment At the end of this
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