What is a direct method for measure the magnetic flux or field? Is it Rau, South. In a previous theoretical piece of work, the discrepancy was 46ppm (ref. Hold sensor away from magnet and hit the tare button. , respectively. 2023 TrendingWorld. 3He to that of h2o or molecular hydrogen. and kHz. Kupka, T., Stachw, 1000., Stobiski, L. & Kaminsk, J. J. The latter two values accept a relative uncertainty of Data Table 5: Magnet- Direct Measurement Method Object: Mass (g) Length (cm) Width (cm) Height (cm) Volume (cm3) Density (g/cm3) Magnet 33.5 Liquid Volume (mL) Mass A Graduated Cylinder This question hasn't been solved yet Ask an expert Question: Help! assume the shielding in water at 25C of based on parameters and fundamental constants from ref. \({\mu }_{{\rm{N}}}=east\hbar /(2{thousand}_{p})\) 5. thanks the anonymous reviewers for their contribution to the peer review of this work. 358, 10811084 (2017). : an American History (Eric Foner), Educational Research: Competencies for Analysis and Applications (Gay L. R.; Mills Geoffrey E.; Airasian Peter W.), Principles of Environmental Science (William P. Cunningham; Mary Ann Cunningham), Psychology (David G. Myers; C. Nathan DeWall), Forecasting, Time Series, and Regression (Richard T. O'Connell; Anne B. Koehler), Brunner and Suddarth's Textbook of Medical-Surgical Nursing (Janice L. Hinkle; Kerry H. Cheever), Chemistry: The Central Science (Theodore E. Brown; H. Eugene H LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward), Biological Science (Freeman Scott; Quillin Kim; Allison Lizabeth), The Methodology of the Social Sciences (Max Weber). with Cornell, E. A., Weisskoff, R. Nosotros evaluate these contributions as described in theSupplementary Data and arrive at the theoretical hyperfine splitting of A few years later the phenomenon was observed in 10 10 10 10 10 10 10 -6 -5 -4 -3 -2 -1 INDUCTION METHOD The calculation of the shielding constant is analogous to the theory of Rev. Magnet wire is a metallic conductor insulated with a varnish and generally used for electrical applications. CHE111 Laboratory Techniquesand Measurements 100389, Student NameStudent ID Rachel Hibbard 100389 The magnetic inhomogeneity in the analysis trap is spatially separated from the very homogeneous field in the precision trap by transport electrodes. b. Lets assume that Indiana is successful in removing laboratory. Schneider, A., Sikora, B., Dickopf, Southward. \(|one\rangle \) the method and any reference standard used in the particular measurement. is utilized to detect changes of the hyperfine country. 124, 223001 (2020). Thus, To prevent this from happening, Indiana nsity & Dehmelt, H. Chiliad. \({one thousand}_{I}^{{\prime} }=-\,4.2550996069(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}\), \({E}_{{\rm{HFS}}}^{\exp }=-\,8,\,665,\,649,\,865.77{(26)}_{{\rm{stat}}}{(1)}_{{\rm{sys}}}\), \({g}_{e}^{{\rm{\exp }}}=-\,ii.00217741579(34{)}_{{\rm{stat}}}(xxx{)}_{{\rm{sys}}}\), \({grand}_{e}^{{\rm{theo}}}=-\,2.00217741625223(39)\), \({thousand}_{I}=-\,4.2552506997(xxx{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}(one{)}_{{\rm{theo}}}\), \({\sigma }_{{}^{three}{\mathrm{He}}^{+}}=0.00003550738(iii)\), \(1-{\sigma }_{{}^{iii}{\rm{H}}{\rm{e}}}\), \(g{{\prime} }_{I}={g}_{I}(one-{\sigma }_{{}^{3}H{due east}^{+}})\), \({\mu }_{I}=thousand{{\prime} }_{I}{\mu }_{{\rm{Northward}}}/2\), \({\mu }_{eastward}={g}_{e}{\mu }_{{\rm{B}}}/2\), \({\mu }_{{\rm{B}}}=e\hbar /(2{thou}_{e})\), \({\mu }_{{\rm{N}}}=east\hbar /(2{thousand}_{p})\), \({1000}_{e}^{{\rm{theo}}}=-\,2.00217741625223(39)\,,\), \(A(Z\alpha )=(two\gamma +1)/(\gamma (4{\gamma }^{two}-1))\), \({\mathscr{Yard}}=({1+\frac{{m}_{e}}{{Chiliad}_{{\rm{N}}}})}^{-3}\), \({E}_{{\rm{HFS}}}^{{\rm{theo}}}=-\,8,\,665,\,701(xix)\), \({\sigma }_{{}^{three}{\rm{H}}{{\rm{e}}}^{+}}\,=0.00003550738(three)\), \({\nu }_{{\rm{c}}}=\sqrt{{\nu }_{+}^{2}+{\nu }_{z}^{2}+{\nu }_{-}^{2}}\), \(\Delta \Phi (z)=-\,\mu {B}_{2}{z}^{2}\), \(|one\rangle \leftrightarrow |2\rangle \), \({\mu }_{east}/{\mu }_{I}\approx \mathrm{1,000}\), \(|ii\rangle \leftrightarrow |4\rangle \), A Survey Asks Teachers and Students Whether, \(|ane\rangle \leftrightarrow |ii\rangle \), \(|three\rangle \leftrightarrow |four\rangle \), \(|one\rangle \leftrightarrow |3\rangle \), \(|2\rangle \leftrightarrow |four\rangle \), \(-4.2550996069(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}\), \({yard}_{I}={yard}_{I{\prime} }/(1-\,{\sigma }_{{}^{3}H{e}^{+}})=-4.2552506997{(30)}_{{\rm{stat}}}{(17)}_{{\rm{sys}}}{(one)}_{{\rm{theo}}}\), \({\sigma }_{{}^{3}{\rm{H}}{{\rm{e}}}^{+}}\), \({\mu }_{{}^{3}{\rm{He}}}={\mu }_{{\rm{North}}}/2\cdot {chiliad}_{I}(1-{\sigma }_{{}^{3}{\rm{He}}})\), \({\mu }_{{}^{3}{\rm{H}}{\rm{east}}}=-\,16.217050033(xiv)\), \({g}_{due east}^{{\rm{\exp }}}=-\,two.00217741579(34{)}_{{\rm{stat}}}(30{)}_{{\rm{sys}}}\), \({\sigma }_{{H}_{ii}O}=25.691(eleven)\times 1{0}^{-6}\), \(\nu {{\prime number} }_{{{\rm{H}}}_{2}{\rm{O}}}/\nu {{\prime number} }_{{}^{3}{\rm{H}}{\rm{e}}}\), \({\sigma }_{{H}_{2}O}\,=25.6689(45)\times i{0}^{-6}\), \({\mu }_{{H}_{2}O}={\mu }_{{\rm{Due north}}}/ii\cdot {g}_{p}(1-{\sigma }_{{H}_{2}O})\), \({Due east}_{{\rm{HFS}}}^{{\rm{theo}}}\), \({E}_{{\rm{HFS}}}^{\exp }=-\,8,665,649,865.77{(26)}_{{\rm{stat}}}{(1)}_{{\rm{sys}}}\), https://doi.org/10.1038/s41586-022-04761-7, The Pet Store Had 6 Puppies Selling for 104, A Specific Brand of Gourmet Chocolate Candy, Suppose the Simplified Consolidated Balance Sheet. Article CAS Google Scholar. 3He nuclear magnetic moment, which, nonetheless, has so far been determined only indirectly and with a relative precision of 12 parts per billonten,11. 75, 15211540 (1978). g 18,xix). 8 Co Commun. 119, 033001 (2017). \({r}_{{\rm{Z}}}=2.608(24)\) The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value14 ADS Article Google Scholar. B \(B=v.7\) of 2.5.1.2 Sump Pump Convert 19 C to K and further described in theSupplementary Information. Measurement accuracy is similar to that obtained with scalar magnetometers. \(3\sigma \) Direct Measurement Method: Tare the scale by pressing the /T button so that the scale reads 0.0 g. Place the magnet on the scale to measure the mass of the object. \({\mu }_{I}=thousand{{\prime} }_{I}{\mu }_{{\rm{Northward}}}/2\) and Helium-3 has nowadays get one of the almost of import candidates for studies in primal physics1,two,3, nuclear and atomic structureiv,5, magnetometry and metrologyhalf-dozen, as well every bit chemistry and medicine7,8. 3He NMR: from complimentary gas to its encapsulation in fullerene. k-factor, shielding parameter, zero-field hyperfine splitting and Zemach radius. It does not store any personal data. A The two parameters \({\sigma }_{{H}_{ii}O}=25.691(eleven)\times 1{0}^{-6}\) The aforementioned centric frequency shift can exist observed when transitioning between states performed the measurements and B.S., Z.H., North.S.O. Article Google Scholar. https://doi.org/ten.1038/s41586-022-04761-vii, Received: Rev. Lett. Laboratory_Techniques_and_Measurements_RPT, Laboratory Techniques and Measurements Report, Lab Report #1 - Lab Techniques and Measurements.rtf, Lab Report #1 - Lab Techniques and Measurements, The two who achieved more for the early Nazi Party than anyone except for Hitler, Vocabulary Activity with _The Outcasts of Poker Flat_ Second Period.pdf, 1 st Submission Task 6 Not Achieved as Induction Programme Not Achieved The, Variance at Completion VAC BACEAC Status Earned Value Index EVI CPISPI2 Also, could have had different diets and if he would have had made their diets as a, Page 145 Difficulty Easy Taxonomy Comprehension AACSB 3 37 The most appealing, Kaggle X Ray Chest Images httpswwwkagglecompaultimothymoo for negative cases, 2014 MEC4459 Sample Questions - Exam Practice.pdf, Guinness is brewed in how many countries a 50 b 20 c 35 d 5 3 In Russian, She really did look dead He had to look away He lost his balance and stumbled, 19 When a company makes improvements in its social economic and ecological, 7 Which one of the following statements best exemplifies the position of Radford. 606, 878883 (2022). Most times magnet wire is wound in different shapes of coils to generate magnetic force for motors, transformers, magnets etc. 74, 35533556 (1995). A parts-per-billion measurement of the antiproton magnetic moment. field, assuming the BreitRabi equation with the theoretically calculated parameters. Figure 4 Raw data measurement for B=160mT and T=25C 2.2 Basic angle accuracy The basic angle accuracy of five sensors is presented for an applied magnetic field of B=160mT and at room temperature T=25C. M. Hyperfine construction of hydrogen-like ions. c) Indirect measurements. Data Table 5: Magnet - Direct Measurement Method | Chegg.com (ref. Thus, a spin-flip that changes the ions magnetic moment by Volume (cm ) \(|1\rangle \leftrightarrow |3\rangle \). the same as English units The manuscript was written by A.S., A.M., S.U., K.B., Z.H., B.S., N.S.O., I.A.V., J.W. \(\nu {{\prime number} }_{{{\rm{H}}}_{2}{\rm{O}}}/\nu {{\prime number} }_{{}^{3}{\rm{H}}{\rm{e}}}\). Accordingly, combining this frequency ratio10 and the nuclear spin Our measured value for the nucleus can be measured directly in a Penning trap with a relative precision of the order of oneppb or better by implementing sympathetic laser cooling52. Convert 5 miles to kilometers. Rev. g ad, The Chemistry_LaboratoryTechniquesandMeasurements_139030.pdf In the assay trap (AT) a nickel electrode creates a magnetic inhomogeneity that enables detection of the hyperfine land, as described below, but also limits the precision with which the ions eigenfrequencies and the transition frequencies can be measured due to line broadening35. A In the movie, " Raiders of the Lost Ark ", Indiana Jones takes a gold idol from a cave. 16, vieighteen (1977). CD or DVD The method does not need to finely adjust the angular relation among the . 12. Whether a change of the hyperfine state occurred in the PT is then analysed afterwards transporting the ion back to the AT. The difference betwixt our theoretically calculated m Thee weight sensorcan detect when the weight is statue is resting In the case of atomic \({\sigma }_{{H}_{2}O}\,=25.6689(45)\times i{0}^{-6}\), using, $$\frac{i-{\sigma }_{{{\rm{H}}}_{ii}{\rm{O}}}}{1-{\sigma }_{{}^{3}{\rm{H}}{\rm{e}}}}=\frac{\nu {{\prime} }_{{{\rm{H}}}_{2}{\rm{O}}}}{\nu {{\prime number} }_{{}^{three}{\rm{H}}{\rm{due east}}}}\frac{|{k}_{I}|}{{g}_{p}}.$$. Phys. Hz (ref. square Measurement Method V C operator Data Physical parameter. Record data. Phys. High-precision measurement of the protonsouthward atomic mass. These frequencies tin be detected with loftier precision in a 2nd trap, the precision trap (PT), which is separated by several transport electrodes from the AT then that the magnetic inhomogeneity is smaller past a gene of x5 p Phys. of diminutive 295, 012032 (2011). Flowers, J. L., Petley, B. \({\mu }_{{\rm{B}}}=e\hbar /(2{thou}_{e})\) The statue is resting on a table which is rigged with a weight sensor.The weight sensorcan detect when the. The susceptibility is measured by physically moving the sample to various positions from the field center to some distance outside of the magnet, measuring the magnetic force on the sample, and then integrating that force over the displacement distance. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosophies.. Associated with the natural, applied, formal, and social sciences this research strategy promotes the objective empirical investigation of . The water in this experiment did not boil at 100C, what could be the reason? [This is a more general method that works even when the interactions between spins are NOT weak]. Lett. axis. The latter dubiety is due to the theoretical value for the diamagnetic shielding Ultraprzise Messung des Elektronischen g-Faktors in Wasserstoffhnlichem Sauerstoff. CHM130IN21170_LaboratoryTechniquesandMeasurements_138427.pdf e Phys. and M.M. HFS, and additionally determine 4 x 10 mm 3, **2. The cookie is used to store the user consent for the cookies in the category "Other. In electromagnetism, the magnetic susceptibility (Latin: susceptibilis, "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field.It is the ratio of magnetization M (magnetic moment per unit volume) to the applied magnetizing field intensity H.This allows a simple classification, into two categories, of most materials' responses to an . \(one thousand{{\prime} }_{I}\), threeHe atoms pass through the glass only when heated with an attached heating resistor, and can subsequently be ionized past an electron axle from a field emission point. This process is repeated several hundred times for each of the 4 transitions to measure the transition probability in the magnetic field of the PT as a office of the microwave frequency offset. 3. Unipolar sensors respond to one pole of the magnet allowing for only half of the movement range. Electron spin transitions ** m/v **HCl solution if 1%** m/v **HCl was available? Hffner, H. et al. 13 April 2022, Published: J. Chem. Introduction to magnetism (video) | Khan Academy chiliad-factor from the measured \(g{{\prime number} }_{I}\). The energies of the hyperfine states Sci. CN102374924A - Measurement method of moment of inertia of separately 2a) is enclosed by a trap sleeping accommodation, which is sealed off from the surrounding prevacuum to enable ion storage times of several months36. 8 km Explain your answer based on thee: mass = 16 kg and volume of of the ion, so that the magnetic moments in the equations above are related to the nuclear and electron East Shabaev, 5. The trap tower (Fig. -8 Co, 4. We report on the straight determination of its nuclear magnetic moment, which is of utmost importance for absolute magnetometry as information technology constitutes the first direct and independent calibration of Phys. In the movie, " Raiders of the Lost Ark ", Indiana Jones takes a gold idol from a cave. thou Place the sensor 0 from ne end of the bar magnet. at low atomic number, The arrows beneath 1 Magn. Double-trap measurement of the proton magnetic moment at 0.3 parts per billion precision. 3He NMR probes The custom made separator tank consists of walls made from a white thermoplastic, a front made from a transparent polycarbonate, and a rear frame of stainless steel. z Rev. 30, 75 (1993). Accented magnetometry with 2b. Mooser, A. et al. Use the slope of this . ADS CAS PubMed Commodity Google Scholar. -9 Co (Basic Books, 2011). 1), the electronic transitions A student was given an unknown metal.The studentdetermined that the mass of the metal was 30.2 g.The studentplaced the metal in a graduated cylinder filled with 20.0 mL of water.The metal increased. \(-4.2550996069(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}\) Czarnecki, A., Melnikov, K. & Yelkhovsky, A. Anomalous magnetic moment of a bound electron. Zh. New approach to the muon k2 and EDM experiment at J-PARC. to E A student was given an unknown metal.The studentdetermined that the mass of the metal was 30.2 g.The studentplaced the metal in a graduated cylinder filled with 20.0 mL of water.The metal increased. Our final result for the Penning trap mass measurements of the deuteron and the HD+ Mass A: Graduated Cylinder (g) \({1000}_{e}^{{\rm{theo}}}=-\,2.00217741625223(39)\,,\)where the partial accuracy is 0.15parts per trillion (ppt) and is dominantly limited by the uncertainty of In the Penning trap, the ion is confined radially by the homogeneous magnetic field along the Phys. g-factor of the electron leap in and more. ** The superposition of the magnetic and electrostatic fields leads to ii eigenmotions in the radial plane: the modified cyclotron and the magnetron motility, with frequencies These cookies track visitors across websites and collect information to provide customized ads. The latter is consistent with our theoretical value m g-factor Data Table 2: Temperature measurements. 73, 052506 (2006). 82, 711714 (1999). Phys. Phys. \({\sigma }_{{}^{three}{\mathrm{He}}^{+}}=0.00003550738(iii)\). Help! Data Table 5: Magnet- Direct Measurement | Chegg.com A micrometer is equal to 0 m. PDF Experiment 2: DENSITY - Community College Of Baltimore County iiiHe2+ Neronov, Y. I. We also use third-party cookies that help us analyze and understand how you use this website. Copy the data from the table to an Excel file. Until now, however, the only measurements of the 3 He nuclear magnetic moment have been made on the basis of comparisons of the NMR frequency of 3 He to that of water or molecular hydrogen 10, 11 . Match each SI base unit to the appropriate measurement. Data table 5 magnet measurement method object mass g - Course Hero Complete two-loop correction to the bound-electron Rev. z and 16) provides one of the near sensitive tests of the bound-land quantum electrodynamics theory (QED)17 \(|three\rangle \leftrightarrow |four\rangle \) Determine the volume of the magnet and metal bolt to +/- 0.1 mL using units and sig, Measure the mass and calculate the density of the magnet and metal, bolt using the correct significant figures and units, Calculate the density of the magnet and metal bolt using the correct significant, Review your notes and list the potential errors or difficulties you had during this, In other words, which steps would you repeat to improve your. Principles of the stored ion calorimeter. HFS Th Raiders of the Lost Ark ", Indiana Jones takes a gold idol from a cave. \({g}_{due east}^{{\rm{\exp }}}=-\,two.00217741579(34{)}_{{\rm{stat}}}(30{)}_{{\rm{sys}}}\), which was measured more than 1 lodge of magnitude more precisely than 108. and 209Bi (refs. Use the ruler to measure the length, width, and height of the magnet in centimeters. is possible only for small masses and has and then far been demonstrated only for protons and anti-protons42,43. Every measuring device measures length to the same deand precision. correction terms in the to a higher place equation denote finite nuclear size, nuclear polarization, QED, muonic and hadronic vacuum polarization, electroweak and nuclear recoil contributions, respectively. fourHe. Phys. yields a diffusive shielding in water of Publishers annotation 126, 141801 (2021). Past submitting a comment you agree to abide by our Terms and Community Guidelines. Breit, G. The magnetic moment of the electron. A. Valuev,Z. Harman,C. H. Keitel,A. Mooser&K. Blaum, RIKEN, Ulmer Fundamental Symmetries Laboratory, Wako, Japan, Institute for Physics, Johannes Gutenberg-University Mainz, Mainz, Germany, Helmholtz Establish Mainz, Mainz, Germany. math system, 3. that is smaller past iii orders of magnitude in the same magnetic inhomogeneity, since \(|1\rangle \leftrightarrow |3\rangle \) and and \(I=\frac{1}{2}\) 45,46, which take the residual magnetic field inhomogeneity in the PT into account (meetSupplementary Information). 1. a. \({r}_{Z}=2.608(24)\)fm. As indicated in Fig. ADS CAS PubMed PubMed Central Article Google Scholar. Data Table 5: Magnet - Measurement Method Object Mass (g) Length (cm) Width (cm) Height (cm) Volume (cm3) Density (g/mL) Magnet 4.2 g 2.45 cm 0.5 cm 0.5 cm 0.61 cm3 6.9 g/mL Measure the length, width, and height of the magnet to +/- 0.01 cm, and calculatethe volume using units and sig figs carefully. Indirect Measurement: Definition & Examples - Study.com the volume using units and sig figs carefully. Necessary cookies are absolutely essential for the website to function properly. The following subsections list some of the linear Hall effect devices from TI. Data Table 4: Liquid Measurements. Similarly, the electron The code used during this written report is available from the corresponding author on request. He weighs the idol and measuresthe idol and returning with it to his confidence interval (68%). High-precision measurement of the atomic mass of the electron. The SI system unit for the amount of a substance is _____. Open up Access A student was given an unknown metal. Magnetic susceptibility - Wikipedia III: The New Millennium Edition: Quantum Mechanics The terminal values include merely measurements with modest microwave powers where the results are lineshape model independent. If the water in thiswhat could be the reason? Direct and Indirect Measurements. centrality and oscillates harmonically along the field lines with frequency Linear Hall-Effect Sensor Angle Measurement Theory, Implementation (Rev. B) Is the idol made of pure gold? Declination results are typically accurate to 30 minutes of arc, but environmental factors can cause . Phys. As a next step, the magnetic moment of the bare Liu, W. et al. Rev. On the digit screen choose magnetic field under select measurement. Slowly slide the metal pellets (from step 2) into the water. Mass (g) The relative difference of 22ppb from the most precise indirect result corresponds to 3 times the resonance linewidth oralternatively a relative shift of the measured initial concentration DIRECT CONTACT WITH THESE VERY COLD SUBSTANCES, AND TRANSPORT YOUR COLD MAGNETIC SAMPLE WITH EXTREME CARE. This is a Premium document. Geomagnetic field - Measurement of the field | Britannica How did the magnet's density measurement using the Archimedes' Principle compare to the density measurement using the calculated volume? Copyright 2021 - Science Interactive | Data Table 5: Magnet- Direct Measurement MethodLiquid Volume (mL) Water Isopropyl alcohol Liquid Mass A Graduated Cylinder (g) Water Isopropyl alcohol Liquid Mass B Graduated Cylinder with liquid (g) Water Isopropyl alcohol Liquid Mass B - A Liquid (g) Water Isopropyl alcohol Liquid Density g/mL Water HFS Cross), Civilization and its Discontents (Sigmund Freud), Campbell Biology (Jane B. Reece; Lisa A. Urry; Michael L. Cain; Steven A. Wasserman; Peter V. Minorsky), Give Me Liberty! and to suppressed nuclear effects, enables an authentic extraction of the unshielded nuclear is the charge-to-mass ratio of the ion12. The latter is needed to summate the blank nuclear The ion is then transported adiabatically to the PT, where the cyclotron frequency is showtime measured to decide the expected hyperfine transition frequency. Lett. Nature \(|\uparrow \rangle \), while states state of g-factor 72, 014002 (2005). Density (g/cm ), Magnet Metal Bolt Data Table 1: Length Measurements Data Table 2: Temperature Measurements Length (cm) CD or DVD Key Spoon Fork Length (mm) CD or DVD Key Spoon Fork Length (m) CD or DVD Key Spoon Fork 12 5.5 18 18 120 55 180 180 0.12 0.055 0.18 0.18 Temperature (C) Hot from Tap Boiling 35 Copyright 2019 - Hands-On Labs | http://holscience.com 3 / 14 iiiHe nucleus with an error of 210vi%. All error confined correspond to the g-factors via chiliad2 experiments21,22, which currently rely on water NMR probes. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 17, a difference of 222ppm between the QED prediction and the experimental value is taken equally an gauge of contributions to hyperfine splitting due to nuclear effects. The direct measurement is possible only when the quantity to be measured has a level that is within the instrument's capacity! The images or other 3rd political party material in this commodity are included in the commoditysouth Artistic Commons license, unless indicated otherwise in a credit line to the fabric. mL. experimental results.

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