ABSTRACT CHARACTERIZING DEFECTS IN STEEL, ALUMINUM AND COPPER BY WAY OF POSITRON ANNIHILATION LIFETIME SPECTROSCOPY. by Jason Lavaska Calloo

Transcription

1 ABSTRACT CHARACTERIZING DEFECTS IN STEEL, ALUMINUM AND COPPER BY WAY OF POSITRON ANNIHILATION LIFETIME SPECTROSCOPY by Jason Lavaska Calloo Machines with moving parts develop wear and tear after some time of operation. Sometimes defects are on the surface, and thus are visible with the naked eye or with a microscope. However, some defects are seated below the surface and are unnoticeable by the human eye or by a microscope. One way of probing materials for these defects is by way of Positron Annihilation Lifetime Spectroscopy (PALS). This sensitive technique was applied to characterize atomic-scale defects in aluminum and copper samples, as well as steel bearing raceways of different levels of usage. Measurements on aluminum and copper were performed before and after annealing near the melting point. Results show that average positron lifetime decreases significantly after annealing. Then steel bearing raceways were subjected to PALS measurements before and after mechanical testing. Results show an average increase in the positron lifetime of tested bearings as compared to the as-fabricated bearing.

2 CHARACTERIZING DEFECTS IN STEEL, ALUMINUM AND COPPER BY WAY OF POSITRON ANNIHILATION LIFETIME SPECTROSCOPY A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirement of the degree of Master of Science in the Department of Physics by Jason Lavaska Calloo Miami University Oxford, Ohio 2011 Advisor Herbert Jaeger Reader Paul Urayama Reader Michael Pechan

3 TABLE OF CONTENTS List of Tables List of Figures Dedication Acknowledgements iv v vii viii Chapter The Positron, Its Interaction with Matter, and Types of Spectroscopy The Exotic Anti-Electron Interaction with Matter Types of Spectroscopy Doppler Broadening of Annihilation Radiation Angular Correlation of Annihilation Radiation Positron Annihilation Lifetime Spectroscopy The Positron Source 6 Chapter Experimental Procedure The Positron Lifetime Spectrometer The Components of the Positron Lifetime Spectrometer Detectors Slow Branch Fast Branch Multichannel Analyzer Time Calibrator Spectrometer Set-up and Calibration 14 Chapter Data Analysis Extracting Lifetimes from the Spectrum Fitting Lifetimes of the Spectrum 18 ii

4 TABLE OF CONTENTS CONTINUED Chapter Results and Discussion Preliminary Experiments Aluminum, Copper and the Sandwich Geometry Overview of the Average Lifetime within Aluminum and Copper The Three Bearings and the Non-Destructive Evaluation Overview of the Average Lifetime within UT, T and TF 34 Chapter Conclusive Remarks Average Lifetime in Aluminum and Copper with the Sandwich Geometry Average Lifetime in the Steel Bearing Raceways with the Non-destructive Evaluation Future Work 37 Appendix A ---- The Gluon Fluid 38 Appendix B ---- Why does a pps annihilate quicker than an ops? 39 Appendix C ---- Conserved Quantities in Radioactive Decays and Nuclear Reactions 42 Glossary 43 References 45 Index 47 iii

5 LIST OF TABLES Table 1-1: Examples of bulk lifetime of positrons in various metals, page 7 Table 4-1: Fitting parameters for preliminary measurements on one of the bearings, page 19 Table 4-2: Fitting parameters for unannealed and annealed aluminum and copper in sandwich geometry, page 21 Table 4-3: Typical fitting results of aluminum in sandwich geometry before annealing, page 22 Table 4-4: Typical fitting results of aluminum in sandwich geometry after annealing, page 23 Table 4-5: Typical fitting results of copper in sandwich geometry before annealing, page 24 Table 4-6: Typical fitting results of copper in sandwich geometry after annealing, page 25 Table 4-7: Fitting parameters for subsequent fits of Untested, Tested and Tested to Failure in NDE geometry, page 30 Table 4-8: Typical fitting results of UT, page 31 Table 4-9: Typical fitting results of T, page 31 Table 4-10: Typical fitting results of TF, page 31 iv

6 LIST OF FIGURES Figure 1-1: A photograph of a positron taken by Anderson in his cloud chamber, page 1 Figure 1-2: Schematic of DBAR circuit, page 4 Figure 1-3: Schematic of ACAR circuit, page 5 Figure 1-4: The decay scheme of 22 Na, page 6 Figure 1-5: The transformation of the proton into a neutron during a β + decay. This happens when an up-quark in the proton changes into a down-quark; thus producing a neutron, a positron and a neutrino, page 7 Figure 2-1: Block diagram of the PAL Spectrometer used in this work, page 9 Figure 2-2: Set-up used for time calibration of MCA, page 13 Figure 2-3: Schematic of the set-up for energy calibration, during which the SCA windows are set, page 15 Figure 3-1: Typical spectrum and its line of best fit. Vertical axis corresponds to number of counts (of positron annihilation events) and horizontal axis corresponds to time (in picoseconds). t 0 for the spectrum is approximately at ps, page 18 Figure 4-1: The sandwich geometry, with source between the (white) sandwiching materials, page 20 Figure 4-2: Sandwich geometry used for aluminum and copper samples, page21 Figure 4-3: Spectrum of unannealed aluminum. Red curve represents line of best fit data, page22 Figure 4-4: Spectrum of annealed aluminum. Red curve represents line of best fit to data, page23 Figure 4-5: Spectrum of unannealed copper. Red curve represents line of best fit to data, page24 Figure 4-6: Spectrum of annealed copper. Red curve represents line of best fit to data, page25 v

7 LIST OF FIGURES CONTINUED Figure 4-7: Dimensions of the bearings, page 28 Figure 4-8: Arrangement for rotational mechanical use of T and TF. Yellow cylindrical bearings remain in contact with inner and outer raceways at all times. Copper-coloured metal shaft is fixed at core. Inner raceway served as sample for tests with PALS during this work, page 29 Figure 4-9: NDE geometry with detectors in light blue, steel bearing in dark blue and positron source in red mounted on (green) lead, page 29 Figure 4-10: Typical spectrum of UT, T and TF with t cal = ps/ch. Red curve represents line of best fit to data, page 30 Figures 4-11: Measurements of average positron lifetimes around circumferences of Untested Bearing UT (a), Tested Bearing T (b), and Tested to Failure Bearing TF (c). Green dashed lines depict average value, page 32 Figure 4-12: Measurements of average positron lifetime around the circumference of Tested to Failure Bearing TF (a), including spall and in the spall only (b). Green lines show average lifetime in vicinity of spall (bottom dashed line) and rest of bearing (top dashed line), page 33 Figure 4-13: Fitted lifetime data of UT, T and TF, comparing the average lifetime of each, page33 Figure B-1a: A clockwise-spinning ball in the classical world, which corresponds to the spindown of a particle in the quantum world, page 39 Figure B-1b: An anticlockwise-spinning ball in the classical world, which corresponds to the spin-up of a particle in the quantum world, page 39 Figure B-2a: With similar spin, the pressure in-between them is higher, page 40 Figure B-2b: With opposite spin, the pressure in-between them is lower, page 40 vi

8 DEDICATION I dedicate this thesis to the two people in the world whom I love the most; more than even God Almighty himself. Those two people are my parents, Lesburn and Marilyn. vii

9 ACKNOWLEDGEMENTS I am very thankful to Dr. Jaeger for teaching me the theoretical and experimental ways of nuclear spectroscopy, and for lending an ear to the miscellaneous questions, including figments of my imagination, that I bring to his office. Thanks to Timken for providing the steel bearing raceways as samples for measurement of positron lifetime, and to Positronics Research, LLC for financial support. Special thanks to Dr. Gerald A. Smith for valuable consultations. Thanks to Michael Eldridge for making the holder of the steel bearing raceways and for providing the aluminum and copper samples. Thanks to Jacob Martin for his efforts to edit parts of the LabVIEW program used in our fitting, and for his help in testing some of the samples. And thanks to my thesis committee members for their time: Dr. Urayama and Dr. Pechan. Imagination is more important than knowledge ---- Albert Einstein viii

10 THE POSITRON, ITS INTERACTION WITH MATTER AND TYPES OF CHAPTER 1 SPECTROSCOPY 1-1 The Exotic Anti-Electron This particle was first predicted by Paul Dirac in 1932 in his dissertation. It was then discovered by Carl Anderson the following year in his particle cloud chamber. The theoretical and experimental works of Dirac and of Anderson confirmed the existence as this anti-particle; thus the first episode of the anti-electron, also known as the positron. The electron had been discovered a few decades earlier in 1897 by Joseph Thompson. Subsequent observations showed that when an electron and a positron interact they are both annihilated, whereby their masses convert to electromagnetic energy. It provided the first experimental proof that mass can be converted to energy and complements Albert Einstein s famous equation E = mc 2. Figure 1-1 is the cloud chamber picture taken by Carl Anderson in 1931, showing a positron entering and passing through a lead plate. A magnetic field is perpendicular to and pointing into the page and the positron is moving upward. This causes the positively charged particle to curve to the left due to the Lorentz Force. Notice the path with less curvature below the plate and the more curved path above it; this means that the positron loses some energy upon penetrating the plate and its path curvature increases. Now this observation revealed that the positron, whose momentum is 1 Figure 1-1: a photograph of a positron taken by Anderson in his cloud chamber [1]

11 directly proportional to the radius of curvature, has the same mass as the electron; 9.1 x kg. The direction of curved motion is opposite that of the electron so it must have the opposite sign of charge; +1.6 x C. Thus the positron is similar to the electron in every way except by sign of charge and by sign of Lepton number; same mass, same spin-½ nature, and same quantity of charge. All anti-particles will annihilate with their counterpart particles. Although the positron by itself is stable, it only has a short time of existence in the universe because of the large supply of electrons in matter. We know that our universe is dominated by matter rather than by antimatter. This presents a puzzle because in the beginning when particles were being formed, there should have been as many anti-particles as there are particles; as many electrons as there are positrons. In other words conserved quantities like Lepton number and Baryon number must hold in all reactions (see Appendix C). Indeed, no matter should be left behind since annihilations would convert everything into electromagnetic radiation. So there seems to be non-conservation and this is an area of active research nowadays [2]. Anyway the fate of this exotic particle goes according to either of these reactions [3]: e - + e + γ + γ Equation 1-1a e - + e + γ + γ + γ Equation 1-1b Emission of two gammas is 370 times more probable than emission of three gammas. [4] 1-2 Interaction with Matter When a positron enters a sample such as a metal, it slows down due to thermalization *. In that process the energy of the impinging positron decreases from a maximum of 540 kev to kev (energy at room temperature). Subsequently the positron will annihilate with an electron and two gamma rays are emitted, typically in a time of 100 to 200 ps. Or the positron can become trapped in a vacancy in the atomic lattice and later annihilate with an electron, usually within 200 to 400 ps. For the two aforementioned encounters of the particles, the time they spend orbiting or exhibiting a positronium-like behavior is negligible. In other words they meet and annihilate right away. In other situations, such as in insulators, the positron and the electron form positronium which is similar to the hydrogen atom with a proton and an electron. There are two types: parapositronium (pps) or ortho-positronium (ops). Equation 1a signifies annihilation of a para- * The time during thermalization (approximately 3 ps) is neglected in lifetime calculations because it is much shorter than the lifetime of positron in matter. 2

12 positronium, and equation 1b represents annihilation of an ortho-positronium. pps has a mean lifetime of 125 ps and annihilates with the emission of two gamma photons, one whose angular momentum is positive and the other of negative angular momentum since they are emitted in opposite directions; thus the net spin of pps is 0. On the other hand ops takes as long as 142 ns to annihilate and emits three gammas, one of negative angular momentum and the other two of positive angular momentum; thus the net spin is 1. The pps takes longer time because the mechanism of emitting three gammas instead of two requires more time (See Appendix B). Sometimes an ops can be transformed into a pps if another electron close to it causes the spin of either the bounded positron or electron to flip. This is called a pick-off ; a mere transformation from an ortho-positronium to a para-positronium by way of spin flipping. 1-3 Types of Positron Spectroscopy A positron will annihilate with an electron when the two interact; two particles of mass are converted to energy. This radiation, which usually involves two quanta of energy 511 kev, is emitted when the particles decay and it fits into the gamma ray end of the electromagnetic spectrum. Currently there are three techniques of observing the spectrum of this radiation. These three methods of positron spectroscopy are categorized as follows: Doppler Broadening of Annihilation Radiation (DBAR) Angular Correlation of Annihilation Radiation (ACAR) Positron Annihilation Lifetime Spectroscopy (PALS) 3

13 1-3-1 Doppler Broadening of Annihilation Radiation This kind of spectroscopy is used to probe the velocity of the electron by way of the Doppler shift of the gamma rays emitted at annihilation. That is, if the particles are moving toward an observer the frequency will appear higher and vice versa. Usually only one of the annihilation gamma ray is sought after by the detector. The detector in use is a Germanium detector because it has a better resolution of energy than a scintillation detector. Thus a distribution of velocities of electrons just before they annihilate can be obtained. Figure 1-2: Schematic of DBAR circuit Angular Correlation of Annihilation Radiation If the electron-positron pair is at rest, the gamma rays emitted at the end of their lifetime move away at an angle of 180 to each other. But often times they are moving (which includes orbiting their common center of mass). As a result of the conservation of energy the gamma rays are emitted at angles less than 180. The technique of ACAR makes use of two detectors, each catching a 511 kev gamma. However, one of the detectors is movable to a position that makes the angle between the two less than 180. So if each detector encounters an annihilation gamma (from the same positron decay) in this configuration of the spectrometer that gives evidence that the particles were moving. This angle is inversely proportional to their momentum. 4

14 Figure 1-3: Schematic of ACAR circuit Each detector comprise of a scintillator and a Photomultiplier Tube (PMT). These components, along with the Single Channel Analyzer (SCA) and the Coincidence will be discussed in Chapter Positron Annihilation Lifetime Spectroscopy PALS is the most frequently used technique of the three. It is also a well-known method of detecting defects of atomic size in material. It requires a signal that indicates the creation of a positron and another which signifies its annihilation. The creation signal comes by way of the gamma ray (of energy 1275 kev) emitted by the 22 Ne when it decays to its ground state and the annihilation gamma (of energy 511 kev) is used to signify the end of the positron s lifetime. A signal of the 1275 kev is used to start a clock, and a signal of the 511 kev is used to stop it. This kind of positron spectroscopy is used in this work to characterize defects in metals. 5

15 1-4 The Positron Source For this work 22 Na was used as the positron source. The source was purchased from Eckert & Ziegler Isotope Products and consists of a small amount of salt ( 22 NaCl) enveloped in a kapton film with an activity of 1.1 MBq (30µCi). One way in which 22 Na is prepared is by bombarding 25 Mg with protons [5] in a cyclotron or high energy accelerator: 25 Mg (p, α) 22 Na 22 Na decays to the excited state of 22 Ne 90.4% of the time by emitting a positron. A subsequent gamma ray (prompt gamma) is emitted with a half life of 3.7 ps and of energy 1275 kev by 22 Ne when making the transition from its excited state to its ground state. 3.7 ps is a very short time compared to measurable lifetimes, which are of order 100 ps. Hence it does not affect the determination of lifetimes. The prompt gamma is the signal that a positron is created (see Figure 1-4), while the annihilation photon (511 kev) signals the end of the positron s lifetime [6]. Figure 1-4: The decay scheme of 22 Na The positrons are emitted with a continuous energy distribution with E = 540 kev [3]. The fact that there is a distribution implies that there is another particle emitted that shares the energy available during the decay. This other particle is the neutrino. So the complete decay is: 22 Na 22 Ne * + e + + ν 22 Ne * has a half-life of 3.7 ps in that excited state and eventually decays to the ground state by emission of a gamma: 22 Ne * 22 Ne + γ Other competing but less probable processes are electron capture and direct transition to the ground state of Ne. 6

16 Due to the sufficiently long half-life of 22 Na the flux of positrons remains constant throughout the experiment, and this source will last for about 7 years. Each side of the (two-sided) kapton film is 25 µm thick, which is thin enough for most of the positrons to make it through (only about 30 to 40% are absorbed) [7]. The lifetime of Figure 1-5: The transformation of the proton into a neutron during a β + decay. This happens when an up-quark in the proton changes into a down-quark; thus producing a neutron, a positron and a neutrino. positrons is a function of electron density; materials with higher electron density typically have a shorter positron lifetime and vice versa. In particular, elements with more electrons on their outer-most shell (orbit) tend to have shorter lifetime of positrons. If an atom is missing from the lattice, for example, a positron can become trapped within that vacancy. That trapped positron takes a longer time to annihilate with an electron. Hence, the so-called bulk lifetime is characteristic for a defect-free material, while a longer lifetime is a feature of vacancy defects. Table 1-1 lists some metals and the average lifetime of positrons in their defect-free bulk [8]. The main purpose of this work is to assemble a PALS spectrometer and use it to measure positron lifetimes in metallic samples, in particular steel bearing raceways before and after mechanical wear. In order to verify that the apparatus is working properly, preliminary measurements on aluminum and copper will be performed Table 1-1: Examples of bulk lifetime of positrons in various metals. Metal Bulk lifetime (ps) Lithium 296 Aluminum 166 Vanadium 125 Copper 122 Tungsten 120 Gold 118 Nickel 110 Iron 107 7

17 EXPERIMENTAL PROCEDURE 2-1 The Positron Lifetime Spectrometer CHAPTER 2 The first task of the spectrometer is to identify the gamma rays emitted during creation and annihilation of the positrons. One detector looks for the 1275 kev quanta (creation signals) while the other detector awaits the 511 kev gammas (annihilation signals). These two signals are used to start and stop a timer which is capable of measuring times on the order of tens of picoseconds. Only events that occur within 500 ns of each other within the resolving time of the timer are considered valid events, and the rest are discarded. They are stored in a histogram of number of events versus lifetime, and the mean lifetime from the spectrum is then determined. Figure 2-1 is a schematic of the spectrometer. The 1275 kev start gamma ray goes into Photomultiplier Tube 1 (PMT 1) and the 511 kev stop gamma ray enters Photomultiplier Tube 2 (PMT 2). Each signal is amplified and then enters a Single Channel Analyzer (SCA) with energy windows set around 1275 and 511 kev for SCA 1 and 2 respectively. Pulses from the SCA s meet at the coincidence unit, which opens the gate only if the signals coincide (see Coincidence). Meanwhile, pulses from PMT s 1 and 2 each pass through Constant Fraction Discriminators (CFD s) 1 and 2, respectively. The Constant Fraction Discriminator determines when a pulse arrives, and shapes it for the Time-to-amplitude Converter (TAC) which is like an electronic picosecond-timer. The pulse from CFD 1 starts the timer and the pulse from CFD 2 stops the timer. Then the output from the timer is stored in the multi-channel analyzer (MCA); that is, only if the gate opens and says yes to the MCA. The delay cable shifts the spectrum from the left corner of the monitor to a few channels over, so that the rise of the spectrum is visible. Each channel corresponds to a range of lifetime, usually 10 to 100 ps per channel. This particular arrangement of the spectrometer is called a fast-slow coincidence because the blue path transmits timing information within nanoseconds while the red path establishes the appropriate energy levels (1275 kev and 511 kev) within microseconds, which is relatively slower than the blue path. 8

18 2-2 The Components of the Positron Lifetime Spectrometer For positron spectroscopy the detectors and complementary elements of the circuit are arranged to identify and transmit signals of gamma rays. Excluding the MCA and the Gate, the remaining components can be categorized into three groups: Detectors (PMT, Scintillator and High Voltage Power Supply in green), Slow Branch (Pre-amplifier, Linear Amplifier, SCA, and Coincidence in red) and Fast Branch (CFD, TAC, and Delay in blue). Figure 2-1: Block diagram of the PAL Spectrometer used in this work Detectors High Voltage Power Supply--- There are two detectors in this work. Each is a coupling of a scintillator (described below) and a Photomultiplier Tube (PMT). The PMT s require a big potential different between their constituent cathode and the anode and it is provided by the high 9

19 voltage power supply, made by Canberra. The value of the voltage can be manually set at will between 0V and 3000V and for this work I had 2200V existing between the cathode and anode plates. Scintillator--- Scintillators are a kind of material that, when struck and penetrated by nucleons, electrons or photons, emit a flash of light (scintillation). The flash of light is due to the excitation and de-excitation of scintillator atoms. This light is collected by the Photomultiplier Tube, where it is converted to a cascade of photoelectrons by way of dynodes placed between a cathode and an anode; thus a photonic signal is converted to an electronic signal. In general a good scintillator should satisfy the following requirements [9]: A material whose atoms are excited and de-excited very quickly by high energy radiation (such as gamma rays) Efficiently convert the incident high frequency radiation to a lower frequency (fluorescence property) Allow transmission of the scintillated photons Generate scintillation light to which the PMT can respond In this work the incident (and excitation) light is a gamma ray and the scintillation light is in the ultraviolet. And the scintillator material is Barium Fluoride crystal (BaF 2 ). Barium Fluoride is used because it has good energy resolution and time resolution simultaneously. Photomultiplier Tube--- This is an electron tube device that is capable of converting light into electronic pulse. It consists of a cathode made of photosensitive material (also called a photocathode) and an anode from which the pulsed signals can be taken. Between the cathodeanode assembly is a ladder of dynodes and each dynode is at a higher potential than the one before it. So when an incident photon from the adjoining scintillator strikes the photocathode an electron is emitted via the photoelectric effect, and that electron is accelerated toward the first dynode. Upon striking that dynode, the electron transfers its energy to other electrons in it. These secondary electrons are then accelerated onto the next dynode along the ladder and release more secondary electrons which are also accelerated; thus resulting in a cascade effect. This cascade effect of electrons dismantling electrons from the dynodes becomes saturated after a while, on the eighth of twelve dynodes, say. At the anode this cascade is collected and results in an output pulse which is used to establish the timing of the absorbed gamma ray. These include organic and inorganic crystals, plastics, glasses and gases. There comes a point when each electron in the cascade can no longer knock off another electron, usually because there is a limit for the amount of electrons that the material of the dynode can give up. Thus, the anode pulse at the output is said to be saturated. 10

20 2-2-2 Slow Branch Preamplifier--- The preamplifier s basic function is to amplify the small voltages (by a factor of 10 to 100 times) that come directly from the dynode of the PMT (see Photomultiplier Tube), and to transmit it through the connecting cable to the linear amplifier (see Linear Amplifier). It is usually mounted close to the PMT and is a part of the circuit that carries energy information [9]. By the time the signal gets to the anode it is saturated and is no longer proportional to the energy of the incident photon. So in order to guarantee a true signal the preamplifier is connected directly to a penultimate dynode before the pulse gets saturated. Linear Amplifier--- The linear amplifier is connected in series to the preamplifier, through which the dynode pulse has been amplified earlier. It has two key functions [9]: Further enhance the signals from the preamplifier Manipulate those signals rapidly and to a convenient form for further processing In order to process the incoming signals quickly, the main amplifier has to briskly bring each pulse to zero. It achieves this by subtracting a portion of each pulse (usually the tail-end) and inverting it. That way the pulse falls to zero quickly after rising to its peak and the energy information is thus preserved. Therefore the main amplifier is able to effectively process and maintain the amplitude of each incoming signal in rapid succession, before transmitting that energy-related information to the Single Channel Analyzer. Single Channel Analyzer--- The Single Channel Analyzer (SCA) is a piece of equipment that sorts incoming signals according to their amplitudes. It does so by way of an adjustable lower level threshold, below which signals are blocked. There is also an adjustable upper level threshold and signals above this mark are discarded. Therefore only signals that fall between these two levels will trigger a response from the SCA. The lower and the upper level threshold form an energy window. Only pulses with amplitudes falling inside the window generate an output pulse from the SCA. Both SCA s are a part of the circuit that anticipates the correct pulses, whose amplitudes are proportional to the magnitude of the energy of the gamma rays; SCA 1 and SCA 2 sift through all incoming signals for the 1275 kev birth pulse and the 511 kev annihilation pulse respectively. Coincidence--- The coincidence unit determines if the two signals transmitted within approximately 500 ns of each other from the SCA s are true or false. Those two signals are the creation and annihilation gamma rays from SCA 1 and 2 respectively. 11

21 2-2-3 Fast Branch Constant Fraction Discriminator--- There is a need to manipulate and transmit signals from the PMT in order to start and stop the TAC. An intuitive technique of discriminating an incoming pulse is called the leading edge discrimination, whereby the discriminator is triggered by the leading edge of an incoming pulse. This kind of discriminator is called the Leading Edge Discriminator (LED). Incoming signals from the PMT may vary in amplitude, however, and pulses of larger amplitudes will usually have an earlier leading edge and vice versa. In turn, larger pulses will trigger the LED first. This results in a false sense of timing for each pulse, because larger pulses will trigger the LED quicker than smaller pulses. Nevertheless, another kind of discriminator called the Differential Constant Fraction Discriminator (DCFD) has the option of setting a window of lower (threshold) and upper levels. Only pulses within the limits trigger an output from the DCFD, and this output signal contains energy and timing information; the leading edge of a pulse determines when a pulse arrives, its amplitude is proportional to and determines energy. On the other hand a Constant Fraction Discriminator (CFD) guarantees a consistent trigger time by taking a constant percentage or fraction of the amplitude of a pulse and inverts it to form a binary pulse. The point where each pulse is bisected is now a common passing point for all of them, regardless of their amplitudes. CFD s are used in this work, that is, in transmitting pulses to the TAC to be used in a start and stop fashion. Delay--- The delay cable is inserted between CFD 2 and the TAC. It shifts the spectrum from the left corner of the monitor to a few channels over, so that the rise of the spectrum is visible. Time-to-amplitude Converter--- The Time-to-amplitude Converter or TAC is a device that converts the time period between the signals from CFD 1 and CFD 2 into an output pulse. The height of this pulse is directly proportional to the duration. CFD 1 starts the TAC and CFD 2 stops it. One way this piece works is to initiate the charging of a capacitor when the start signal arrives, and then to terminate this charge when the stop signal is triggered, for which the formula is: Equation 2-1 For very small times, t, this equation becomes after applying the Taylor Series expansion of and taking the first two terms. This means the capacitor charges linearly within the first few nanoseconds. Since the charging is initiated and terminated within this period then the voltage becomes linearly proportional to time, and the MCA obtains this time-frame. With the TAC output digitized in binary code, its decimal equivalent becomes the channel number in which the data point is deposited. 12

22 2-2-4 Multichannel Analyzer This device makes a record of number of events (vertical axis) versus time (horizontal axis). The MCA used in this work contains 8191 channels or bins into which events are stored in histogram format. Each channel has a certain width in time which depends on the time calibration (see Time Calibrator), and when the MCA receives the signal of a count ** from the gate it puts a data point into a bin that corresponds to that time-frame. That time-frame is dependent on the time that the TAC has to wait for start and stop signals (see TAC). The gate is triggered by an input logic signal from the coincidence (see Coincidence). If the logic is true the gate opens and conveys this information to the MCA Time Calibrator To determine the width (in time) of each channel of the MCA the time calibrator is used. It is connected to the start and to the stop inputs of the TAC, through which signals are generated at regular intervals. Since the MCA has to be triggered by the TAC, peaks at regular intervals are in turn generated among its channels. The centroid of these peaks are then determined, which correspond to certain channel numbers, and a plot is made of those channel numbers with respect to the time between them. This plot is a straight line and its slope gives the time calibration in ps/ch. The time calibration used in this work was near 10 ps/ch for preliminary measurements of lifetimes, and subsequently changed to approximately 50 ps/ch. Figure 2-2: Set-up used for time calibration of MCA ** A count is acquired when the creation gamma of 1275 kev and the annihilation gamma of 511 kev are from the same positron-electron pair. It is valid only when the gate opens and releases that information to the MCA. 13

23 2-3 Spectrometer Set-up and Calibration Effective operation of the spectrometer of this work includes acquiring, transmitting and processing signals from gamma rays; gamma rays that correspond to the creation and annihilation of positrons. And maximizing this efficiency includes appropriately spacing the detectors, tuning the CFD s and the SCA s, determining the resolution of the detectors, and finding the channel for which t = 0 by way of the prompt peak. The spacing between the two detectors had to be optimized. If they are too close to each other counts of valid events could be accumulated quickly, but along with many invalid events. On the other hand, if they are too far apart valid events might be accumulated at a slower rate, but with fewer invalid events. The optimal distance between the detectors was found to be 16 cm. This distance depends on the activity of the source and how well the sample absorbs gamma rays. The source and sample were placed in sandwich geometry in the central spot, 8 cm from either detector. The quality of the resolution of the instrument depends on the type and thickness of the scintillation crystal being used and on the quality and adjustments of the coincidence electronics. The scintillation material is Barium Fluoride crystal (BaF 2 ) and it is used because it has good energy resolution and time resolution simultaneously. It s cylindrical in shape with a diameter of 5 cm and a length of 2.5 cm. This property also depends on the time it takes the incident gamma photon on the Barium-Fluoride crystal to lose its energy. This energy is lost by way of Compton scattering and of exciting the atoms in the lattice, which emit photons of less energy, usually in the ultra-violet. This time of finest resolution of my spectrometer is approximately 415 ps at the moment. That is, the spectrometer is able to discern events that happen in the time frame of 415 ps or longer. Determining the resolution of the instrument is also imperative and the isotope 60 Co was used. It decays by emitting two gamma rays simultaneously (within 0.7 picoseconds of each other [10]) and the detectors are set to identify coincidences of that event. The spectrum acquired is fittingly called a prompt peak since the gamma rays are emitted sequentially, one immediately after the other. The centroid of the prompt peak helps to determine where the t = 0 channel is located. It has the shape of a Gaussian curve and its Full Width at Half Maximum (FWHM) represents the resolution time of the spectrometer. Time calibration of the spectrometer multiplied by FWHM of the prompt peak gives the resolution of the instrument, usually on the order of 100 s of picoseconds. As mentioned earlier 415 ps is the resolution of the spectrometer in this work. For example, CFD s (Constant Fraction Discriminators) give better time resolution than LED s (Leading Edge Discriminators). Usually a spectrometer can distinguish events in a time frame of a fraction of their labeled time. So the detectors used in this work are able to detect less than 415 ps. 14

24 Another step in calibrating the spectrometer is optimizing the settings of the CFD s. In particular the threshold knob on each CFD was adjusted until an optimum was achieved. That optimum value is the Full Width at Half Maximum (FWHM) of the peak on the monitor display. That value improved from 11.5 channels to 8.5 channels. Additionally, the length of the delay cable of each CFD was suitably chosen to match (between 10% and 90% of) the rise-time of the pulses being delayed; signals are delayed approximately 1.5 ns/ft by the cable, which corresponds to a length of 7 in. Settings of the knobs corresponding to windows of the Single Channel Analyzers (SCA s) were also adjusted by way of the set-up depicted in Figure 2-3. Initially, with the gate disconnected from the MCA input (or SCA output), the entire energy spectrum can be seen on the monitor; that is, peaks that represent the 511 kev and the 1275 kev respectively. Then the gate can be reconnected and the upper level of the window of SCA 1 can be lowered and the lower one can be raised so that the 1275 kev is the only peak emerging through that window. Likewise the gate is connected to SCA 2 and the procedure of lowering and rising is repeated. So the window of each SCA is set separately, and one-at-a-time. This is also known as energy calibration. Figure 2-3: Schematic of the set-up for energy calibration, during which the windows of the SCA are set Not to be confused with the delay cable that connects the output of CFD 2 to the stop input of TAC. 15

25 DATA ANALYSIS CHAPTER Extracting Lifetimes from the Spectrum Extracting physically meaningful information from a spectrum acquired by way of PALS is a key intention of this work; particularly, information about lifetime of positrons in a metal. Preliminary steps to achieve this include appropriate set-up of the spectrometer as mentioned before, and also making use of a computer program to measure the lifetimes. If the spectrometer had a perfect time resolution then a spectrum with one lifetime would have the form: Equation 3-1 where t 0 is the t = 0 channel, τ is the lifetime, A 0 is the number of counts at t = t 0, and B is the number of background counts. If there are N lifetimes, due to positrons annihilating in several environments, then the equation becomes: Equation 3-2 If the lifetimes are significantly different from each other then the exponential is turned into straight line segments by way of a semi-log plot. Amidst these segments there are several distinguishable slopes. The spectrometer generally does not have a perfect resolution. It is instead finite, and is often well described by a Gaussian of width σ and centroid t 0. The spectrum then has the form: Equation 3-3 This is the function to which the lifetime spectrum needs to be fitted [6]. Counts less than t 0 occur via unrelated events, that is, when a start signal occurs before a stop signal. The erf means error function and it is a part of the result when a Gaussian function is integrated. 1-erf is the complementary error function and it serves as a means to guarantee that counts are rendered positive and are incremented in the positive direction of the counts axis. After all, a count cannot 16

26 be less than zero. The actual fit was performed using the Levenberg Marquardt Algorithm (LMA) available on LabVIEW. Fitting is done by the method of minimizing the chi-squared function. This method involves subtracting the calculated data points from the measured data points, squaring the result and dividing by the calculated data points, thus minimizing the sum over all data points: Equation 3-4 where y data = measured data points, y fit = calculated data points. In order to minimize the sum over the data points, as mentioned earlier, the process has to be done by way of iteration. LMA locates the minimum of a function with respect to a number of parameters through this iterative process; that is, it changes the value of the parameters iteratively until they are minimized. Minimizing that value in turn causes the red curve (calculated data) to outline or fit the yellow data points (measured data) closely, as depicted in Figure 3-1. The quality of the fit is judged by the value of the reduced chi-squared, which is just the chi-squared divided by the degrees of freedom; degrees of freedom is number of measured data points (y data ) minus the number of fitting parameters [21]. A rule of thumb is that a reduced chi-squared much larger than 1 indicates a poor fit, or in other words, the red fitted curve does not fully capture the yellow data points in Figure 3-1. While a value close to or smaller than 1 indicates a good fit. The fitting program used in this work, which integrates LMA as the key component, was created on LabVIEW and is able to fit up to four lifetime components. The parameters involved in analyzing data include as many as: four lifetime components (τ 1, τ 2, τ 3 and τ 4), four intensity components (A 1, A 2, A 3 and A 4 ), a background (B), and two parameters from the resolution function (width σ or FWHM and centroid t 0 ). It is customary to express the lifetime components in terms normalized intensities I 1, I 2, I 3 and I 4. The intensities are defined as: Equation 3-5 so that the Σ I i = 1. Since the spectrum consists of up to four slopes, each slope is associated with a lifetime of positrons. For example, one component represents lifetime of positrons in the metal sample, another component represents annihilation in the source itself, and the other components represent annihilation in the kapton encasing the source. A background is generated due to random coincidences between unrelated events, and also due to Compton scattering of the gamma rays with the surroundings. 17

27 Figure 3-1: Typical spectrum and its line of best fit. Vertical axis corresponds to number of counts (of positron annihilation events) and horizontal axis corresponds to time (in picoseconds). t 0 for the spectrum is approximately at ps. 3-2 Fitting Lifetimes of the Spectrum Consider a sample material with a bulk (or defect-free) lifetime, one defect lifetime in the form of a single atomic vacancy (or a cluster of vacancies) ***, and a lifetime component due to the source; altogether, three lifetimes. Now, an attempt can be made to fit all three lifetimes individually and to do this requires a spectrometer of resolution 200 ps or less. Furthermore this is usually possible only if the three components differ by more than 10 to 20 ps. Otherwise, the spectrometer will not be able to resolve the difference between the lifetime of the bulk and lifetime of the defect. Another alternative, especially if meticulous preparation of the sample material is not feasible, is to fit a small number of lifetimes (typically three or four) that describe the spectrum as best as possible and then to determine the average lifetime. As mentioned earlier, there is a possibility that the values of the lifetimes are very close and beyond resolution of the spectrometer. The sample materials for this work had little or no purification, so the approach of averaging the three or four lifetimes that best describes the spectrum is brought into play. *** Higher order defects are more likely to occur at high temperatures, such as close to the melting point of a material. Attempts to anneal aluminum and copper were made, but there still lingers several defected lifetime components. 18

28 RESULTS AND DISCUSSION 4-1 Preliminary Experiments CHAPTER 4 A convenient time calibration of the width of the channels of the MCA was required and to determine this, preliminary tests for defects via PALS was done on one of the sample steel bearing raceways, and the calibration used then was 9.78 ps/ch and the complementary parameters are placed in Table 4-1. Table 4-1: Fitting parameters for preliminary measurements on one of the bearings. Full Width at Half Maximum (FWHM) ± 0.08 ch Time calibration (t cal ) 9.78 ± 0.03 ps/ch (t 0 ) 1418 ± 4 ch Resolution 433 ± 2 ps Fitting range 1444 ch to 3000 ch Subsequent measurements on the sample was repeated with a time calibration of 46.39ps/ch. Implementing ps/ch gave way to accumulating more counts per channel, while 9.78ps/ch gave less counts per channel for the same configuration of the detectors and activity of the isotope. To illustrate the effect that the time calibration has on counts, compare the amount of counts accumulated for the sample via each calibration value within the same time-period of approximately 4 hours. Within the first 10 channels after t counts were available by way of a time calibration of 9.78 ps/ch, whereas counts were obtained by way of ps/ch; about 4 times as many counts. 19

29 4-2 Aluminum, Copper and the Sandwich Geometry In the sandwich geometry identical pieces of a material are used to sandwich the positron source. A sandwich implies that the sample to be tested is cut into halves, which become the sandwich. Otherwise identical pieces have to be acquired. It is the most effective geometry because positrons are guaranteed to enter both pieces of the surrounding material. Some positrons, however, will also annihilate in the source and in the kapton that encases it. This configuration is shown in Figure 4-1. To implement the sandwich geometry two identical strips of aluminum and of copper were acquired from the machine shop and served as the sandwich of the isotope. Superficially they appeared to be pure but positron lifetime within told a different story. The lifetime of positrons in the metals were measured with the spectrometer. The resulting spectra are shown in Figures 4-3 through 4-6 and the parameters that are used for the fit are listed in Table 4-1. An average lifetime that disagreed with the theoretical bulk Figure 4-1: The sandwich geometry, with source between the (white) sandwiching materials value was observed, which implied that the strips contained defects on the atomic scale. Average lifetimes are calculated by way of the equation: Equation 4-1 Results are engraved in Tables 4-3 through

30 The pieces of aluminum were approximately 60 mm long, 15 mm wide and 5 mm thick. They were placed in a glass tube, which was sealed afterward and evacuated by way of a depressurizing mechanical pump. Pressure within the tube was decreased to approximately 3000 Pa (or about 23 torr). Then, with the metal sample still inside the glass tube, this amalgamation was placed in a furnace to be annealed. The furnace and its contents began at room temperature and digital settings of the furnace allowed a gradual increase of the temperature from 25ºC to the annealing temperature of 550 C. The gradual increase was timed for 6 hours, and the annealing temperature was maintained for an additional 60 hours. Then it was also cooled to room temperature for 6 hours. This procedure was repeated for a pair of copper strips, whose dimensions are approximately 60 mm 10 mm 5 mm. The annealing temperature for the copper strips was 830 C. Then another set of measurement of lifetime was performed on the annealed metals. Figure 4-2: Sandwich geometry used for aluminum and copper samples Table 4-2: Fitting parameters for unannealed and annealed aluminum and copper in sandwich geometry. Full Width at Half Maximum (FWHM) 8.94 ± 0.07ch Time calibration (t cal ) ± 0.06 ps/ch (t 0 ) ± 0.5 ch Resolution 415 ± 3 ps Fitting range 309 ch to 909 ch The value for the annealing temperature is three quarters of the absolute melting temperature. 21

31 Counts Time (ps) Figure 4-3: Spectrum of unannealed aluminum. Red curve represents line of best fit data. Table 4-3: Typical fitting results of aluminum in sandwich geometry before annealing. Lifetime one (τ 1 ) 279 ± 4 ps Intensity one (I 1 ) 79 ± 3 % Lifetime two (τ 2 ) 597 ± 41 ps Intensity two (I 2 ) 12 ± 3 % Lifetime three (τ 3 ) 2385 ± 24 ps Intensity three (I 3 ) 9.0 ± 0.4 % Background 149 ± 1 count Reduced chi-squared 1.1 Average lifetime (τ average ) 506 ± 22 ps 22

32 Counts Time (ps) Figure 4-4: Spectrum of annealed aluminum. Red curve represents line of best fit to data. Table 4-4: Typical fitting results of aluminum in sandwich geometry after annealing. Lifetime one (τ 1 ) 169 ± 3 ps Intensity one (I 1 ) 55 ± 1 % Lifetime two (τ 2 ) 360 ± 4 ps Intensity two (I 2 ) 42 ± 2 % Lifetime three (τ 3 ) 1486 ± 17 ps Intensity three (I 3 ) 2.0 ± 0.1 % Background 562 ± 2 counts Reduced chi-squared 1.4 Average lifetime (τ average ) 282 ± 4 ps 23

33 Counts Time (ps) Figure 4-5: Spectrum of unannealed copper. Red curve represents line of best fit to data. Table 4-5: Typical fitting results of copper in sandwich geometry before annealing. Lifetime one (τ 1 ) 197 ± 9 ps Intensity one (I 1 ) 62 ± 5 % Lifetime two (τ 2 ) 422 ± 15 ps Intensity two (I 2 ) 36 ± 5 % Lifetime three (τ 3 ) 1975 ± 108 ps Intensity three (I 3 ) 2 ± 0.3 % Background 43.0 ± 0.4 counts Reduced chi-squared 1.0 Average lifetime (τ average ) 307 ± 14 ps 24

34 Counts Time (ps) Figure 4-6: Spectrum of annealed copper. Red curve represents line of best fit to data. Table 4-6: Typical fitting results of copper in sandwich geometry after annealing. Lifetime one (τ 1 ) 164 ± 2 ps Intensity one (I 1 ) 64 ± 2 % Lifetime two (τ 2 ) 396 ± 4 ps Intensity two (I 2 ) 35 ± 1 % Lifetime three (τ 3 ) 2289 ± 80 ps Intensity three (I 3 ) 1.0 ± 0.1 % Background 1426 ± 2 counts Reduced chi-squared 1.3 Average lifetime (τ average ) 267 ± 5 ps 25

35 4-3 Overview of the Average Lifetime within Aluminum and Copper In Tables 4-3 through 4-6 τ 1, τ 2 and τ 3 represent positron lifetime in the bulk + small defects, source + greater defects, and positronium lifetime in kapton encasing the source respectively; I 1, I 2 and I 3 represent intensities that go with those lifetimes. The bulk lifetime of the metals is not distinguishable because (1) values of approximately 100 s of ps are too far below the resolution of the spectrometer and (2) there might be so many defects that very few positrons annihilate in the bulk, and they therefore annihilate in a defect instead. So even τ 1 is already an average of bulk + small defects. From Table 4-3 the average lifetime for the unannealed aluminum is 506 ± 22 ps and from Table 4-4 the average lifetime of the annealed aluminum is 282 ± 4 ps. Also from Table4-4, the value of τ 1 for the annealed aluminum is 169 ps, which is very close to the theoretical value listed in Table 1-1! This implies that the spectrometer was able to distinguish the characteristic bulk lifetime of the annealed aluminum. The corresponding average lifetime for the unannealed copper is, from Table 4-5, 307±14ps. On the other hand, the average lifetime for the annealed copper, as given in Table 4-6, is 267 ± 5 ps, which indicates that the annealing process removed some of the defects. The theoretical bulk lifetime copper is 122 ps (see Table 1-1) and the value measured by our spectrometer is 164 ps. This shortcoming of not acquiring that theoretical value for annealed copper is more likely due to resolution limitations of the spectrometer, or the annealing didn t remove all the defects. Obviously there is a significant decrease in the mean lifetimes of positrons in each metal and it proves that the annealing process was successful in eliminating some of the defects in the form of atomic vacancies. The value of the background accumulated during the test of the unannealed aluminum (Table 4-3) is lower than the background of the annealed aluminum (Table 4-4) because the latter was run for a longer time. Likewise this explains the difference between the backgrounds (Table 4-5 and 4-6) of the unannealed and annealed copper data. The value for intensities of the source contribution acquired by other PALS experimentalists are within 15 to 20% [7], and the corresponding thickness of the kapton used in their work was 7µm. By comparison to this work, the intensities of the source contributions of the annealed metals, of Tables 4-4 to 4-6, are large due to the relatively thick layer of kapton and also due to defects. The layer of kapton in this work is 25 µm thick and the I 2 alone is between 30 and 40%. The relative I 2 and I 3 of annealed aluminum, annealed copper and unannealed copper are between 30 to 40% and 1 to 2% respectively. However I 2 and I 3 for the unannealed aluminum are 12% and 9%. This relatively low value of the source contribution of the unannealed aluminum is not understood. 26

36 Nonetheless, the values of τ 1 and τ 2 for unannealed aluminum and copper are consistent with other literature values by PALS experimentalists [12]. For example, for one vacancy defect in aluminum, resulting lifetime of positrons therein (for τ 1 ) is 253 ps [12], [13], and for four vacancy defects positrons lifetime is 329 ps [12], [13]. The actual source intensity contributions from the salt and the kapton (I 2 and I 3) and the corresponding salt and kapton lifetimes (τ 2 and τ 3) are not expected to change very much throughout the experiment. From other experimentalists literature, the value of τ 2 after the annealing process is typically 360 to 460 ps, and τ 3 is usually between 1400 to 3000 ps [7], [14], [15], [16]. So since τ 2 and τ 3 are basically constant, then any change in the average lifetime, τ average, is due to the variation in defects from metal to metal. 4-4 The Three Bearings and the Non-Destructive Evaluation Steel bearing raceways are an effective mechanical assembly when it comes to executing rotational motion. They are practically frictionless especially when lubricated, and their loadbearing capacity is impressive. One way of manufacturing these steel bearing raceways is by way of cutting a long steel shaft into smaller pieces. Then a lathe can be used to carefully bore and shape the piece to design specifications. Furthermore these raceways can also serve as miniature models for larger-scale applications, such as the ball bearing component within windmill turbines, motor vehicle wheels and drive shafts, crank shafts of engine blocks, etc. Unquestionably, there is a perpetual and increasing need for bearing raceways to function in a dependable manner. For example, rotating parts of an assembly need to do so without slipping off, with as little friction as possible, with enough strength to support a required load capacity, with a reasonably long lifetime, etc. However, even the most robust bearings are not immune to the various sources of surface stress and fatigue: insufficient lubrication, dust contamination, overloading, etc. [17]. So there arises the need identify defects in a timely manner so as to avoid potentially catastrophic failure. Positron Annihilation Lifetime Spectroscopy was used to characterize atomic-size defects in steel bearing raceways. The steel bearing raceways of this work were supplied by Timken. The diameter of each bearing is 80 mm; thickness and height are 8 mm and 35 mm respectively (see Figure 4-7). Each has a mass of 545g. On their outer surfaces cylindrical rollers were set to roll, with immense pressure and stress between the surface of the raceway and the surfaces of the cylindrical bearings. During their usage a metal shaft was fixed at the core of the inner raceway Timken specializes in manufacturing steel parts and bearings for a variety of applications: automobile drive trains, windmills, railway tracks, etc 27

37 (see Figure 4-8). Over time, this rotational friction generated defects. The bearing raceways were labeled as Untested (UT), Tested (T) and Tested to Failure (TF). TF and T underwent this wear from usage, with ensuing damages while UT was not subjected to any testing. Since no mechanical usage was performed on UT, the assumption is made that defects are only due to the fabrication process. On the other hand, T and TF were used after fabrication for the same period of time, and therefore accumulated defects from the mechanical wear. This time period is unbeknownst to us, but since TF developed a spall during use it might have been subjected to a more vigorous use. The spall developed is 10 mm long, 2 mm wide and 0.7 mm deep. Measurements on UT, T and TF were done via nondestructive evaluation (NDE) geometry, whereby the source was mounted on a reference material. The reference material used in this work was lead, and measurements were performed with the radioactive source placed upon the samples, virtually touching them, as depicted in Figures 4-9. The sandwich geometry cannot be used in this situation because (1) the bearings are not able to form a sandwich, and (2) they were not allowed to be cut into sandwichable halves. The fit was made to three lifetimes and the average lifetimes was procured from such; again by way of Equation 4-1. The average lifetime of positrons around the circumference of each steel bearing sample was measured via PALS, and using NDE. The fitting parameters of Table 4-7 were used, and the results are tabulated throughout Tables 4-8 to The zero angle for UT and T were arbitrarily chosen on their circumference. For TF however, the zero angle was chosen to be the center of the spall. The angle subtended by the gash was roughly 2 (that is, 1 on each side of the zero mark of the gash). 8 mm 80 mm 35 mm Figure 4-7: Dimensions of the bearings 28

38 Figure 4-8: Arrangement for rotational mechanical use of T and TF. Yellow cylindrical bearings remain in contact with inner and outer raceways at all times. Copper-coloured metal shaft is fixed at core. Inner raceway served as sample for tests with PALS during this work. Figure 4-9: NDE geometry with detectors in light blue, steel bearing in grey and positron source in red mounted on (green) lead. 29

39 Counts Table 4-7: Fitting parameters for subsequent fits of Untested, Tested and Tested to Failure Bearings in NDE geometry Full Width at Half Maximum (FWHM) 8.94 ± 0.07ch Time calibration (t cal ) ± 0.06 ps/ch (t 0 ) ± 0.5 ch Resolution 415 ± 3 ps Fitting range 309 ch to 606 ch Data Fit Time (ps) Figure 4-10: Typical spectrum of UT, T and TF with t cal = ps/ch. Red curve represents line of best fit to data. 30

40 Table 4-8: Typical fitting results of UT. Lifetime one (τ 1 ) 216 ± 31 ps Intensity one (I 1 ) 64 ± 2 % Lifetime two (τ 2 ) 461 ± 72 ps Intensity two (I 2 ) 33 ± 2 % Lifetime three (τ 3 ) 2319 ± 486 ps Intensity three (I 3 ) 3 ± 1 % Background 9.7 ± 0.4 counts Reduced chi-squared Average lifetime (τ average ) 362 ± 63 ps Table 4-9: Typical fitting results of T. Lifetime one (τ 1 ) 193 ± 12 ps Intensity one (I 1 ) 60 ± 8 % Lifetime two (τ 2 ) 452 ± 21 ps Intensity two (I 2 ) 36 ± 10 % Lifetime three (τ 3 ) 3248 ± 357 ps Intensity three (I 3 ) 4 ± 1 % Background 28 ± 2 counts Reduced chi-squared 1.14 Average lifetime (τ average ) 441 ± 42 ps Table 4-10: Typical fitting results of TF. Lifetime one (τ 1 ) 254 ± 11 ps Intensity one (I 1 ) 61 ± 4 % Lifetime two (τ 2 ) 532 ± 32 ps Intensity two (I 2 ) 36 ± 5 % Lifetime three (τ 3 ) 4917 ± 437 ps Intensity three (I 3 ) 4 ± 1 % Background 46.7 ± 0.3 counts Reduced chi-squared 1.06 Average lifetime (τ average ) 534 ± 51 ps 31

41 τ-average (ps) τ-average (ps) τ-average (ps) (a) Angle ( ) (b) Angle ( ) (c) Angle ( ) Figures 4-11: Measurements of average positron lifetimes around circumferences of Untested Bearing UT (a), Tested Bearing T (b), and Tested to Failure Bearing TF (c). Green dashed lines depict average value. 32

42 τ-average (ps) τ-average (ps) τ-average (ps) Angle ( ) Angle ( ) Figure 4-12: Measurements of average positron lifetime around the circumference of Tested to Failure Bearing TF, including spall (a) and in the spall only (b). Green lines show average lifetime in vicinity of spall (bottom dashed line) and rest of bearing (top dashed line) UT T TF Bearing Figure 4-13: Fitted lifetime data of UT, T and TF, comparing the average lifetime of each. 33

43 4-5 Overview of the Average Lifetime within UT, T and TF The average lifetime of positrons in UT turned out to be 363 ± 23 ps. Typically in pure steel, theoretical lifetimes range from 105 to 110 ps. However, this time range is not resolvable by the spectrometer. And what is more, there might be so many vacancies that the chances of a positron annihilating in the bulk is slim to none. These defects though, are due to the fabrication process of the raceway. So the average lifetime value of 363 ps already includes the bulk + fabrication defects, and UT thus forms the baseline from which the average lifetime of T and TF can be compared. The average lifetime of T was 436 ± 19 ps. This assessment reflected defects accumulated via, not only the fabrication process, but also wear and tear from the earlier mechanical test. Annihilation of positrons within the bulk is deemed irresolvable and/or drowned by the abundance of defects. In other words, due to a high level of defect concentration positrons had the tendency to become trapped and annihilate in a defect rather than in the bulk. Measurements of the average lifetime around the circumference of TF excluding the gash turned out to be 501 ± 19 ps. This value implies, even as before for T, that there is a high defect concentration along the surface of the bearing. As mentioned before, these defects are a combination of fabrication and mechanical wear. Thus, positrons were less likely to decay in the bulk. On the other hand, the average lifetime within the vicinity of the gash of TF turned out to be 426 ± 9 ps, which is significantly lower than 501 ps for outside the gash. This value also implies decay in an area of the lattice containing many defects. This seems contradictory since positron lifetime should increase wherever there is a higher defect concentration. So by intuition the average lifetime should be higher within the gash. PALS is not needed to test for defects at that area of the gash since it is visibly defected by the human eye. However, the immediate microscopic layer below the visible gash should contain atomic vacancies, and this deficiency should have been reflected in the average lifetime thereof. This anomaly of the spall of TF having a smaller average lifetime than the rest of TF cannot be explained at this time. The gash is also somehow magnetized, so maybe that leads to one of several questions: Could the magnetic field within the gash have an effect on the positrons lifetime? Specifically, could the Lorentz Force generated by the bearing s magnetic field cause of a coupling to the Coulomb Force and thus hasten the interaction between the electron and the positron? Or could the removal of that chunk which caused the spall result in a compression of the subcutaneous lattices, thus decreasing the lifetime of positrons in those layers? 34

44 T and TF were used for a similar amount of time. It seems however, that TF was used under more extreme conditions or there were variations in the tools used for fabrication. Could there have been abnormalities during that process? So being, then more samples from each stage of the three cycles (Untested, Tested, and Tested to Failure) have to be included in the experimental runs via PALS. For example, perhaps 10 Untested Bearings, 10 Tested Bearings and 10 Tested to Failure Bearings have to be systematically measured for atomic defects. If the anomaly concerning lifetime in the gash persists, then that implies that some unforeseen property of the material is indeed affecting the positron decay. Otherwise, this phenomenon with TF might just be a one-in-a-million happenstance. 35

45 CONCLUSIVE CHAPTER REMARKS 5-1 Average Lifetime in Aluminum and Copper with the Sandwich Geometry 5 The average lifetime procured from the measurement of the unannealed aluminum turned out to be 506 ps (see Table 4-3). On the other hand, the average lifetime within the annealed aluminum is 282 ps (see Table 4-4). From this comparison there is a significant decrease between the average lifetimes of the sample in each stage; τ average before annealing is much higher than after annealing. The average lifetime within the copper before annealing was 307 ps (see Table 4-5) while the average lifetime after annealing turned out to be 267 ps (see Table 4-6). This also shows a significant decrease in τ average before and after the annealing process, and so extinguishing some of the atomic vacancies was successful. 5-2 Average Lifetime in the Steel Bearing Raceways with the Non-destructive Evaluation From Figure 4-13 the average lifetime of positrons around the circumference of UT is 363 ps. This value, as mentioned before, includes lifetime of positrons in defects + bulk. And these defects are caused by the process or processes of fabrication. 363 ps can then considered to be the baseline average lifetime of positrons within the three raceways. Unlike UT, T underwent mechanical tests and defects incurred therein (on the outer surface) are reflected in its τ average. This value of 436 ps, even as scripted in Figure 4-13, proves that the mechanical wear adds to the increase in τ average for T. Finally the average lifetime of positrons in TF showed significant increase, as compared to both T and UT. The data point corresponding to 501 ps on Figure 4-13 is ample evidence that TF contains more defects. Thus characterizing defects in each of the three bearing raceways was successful: the Untested Bearing has fatigues due to fabrication, which is unavoidable from the manufacturer s point-of-view. Tested Bearing and the Tested to Failure Bearing had additional defects via mechanical wear, and the trend of average positron lifetime within them increased. 36

46 5-3 Future Work If a systematic testing was done on each steel bearing raceway, especially on T and on TF, between different stages in their mechanical use then a more detailed conclusion can be drawn about how wear affects lifetime. In other words, how much time does it take for a raceway to accumulate enough atomic defects via mechanical wear to the point where it is condemned? Tests with PALS in the future may include this endeavor. In order to consolidate the claim even further, that TF contains greater defects than T, then a wide assembly of bearings may also be acquired from each stage; say 10 T s and 10 TF s. There might be statistical variations among the bearings of each stage, which might cause the lifetimes of either bearing to overlap or deviate farther from each other. Efforts to improve the resolution of the spectrometer can be continued for later works. Is there a different scintillator with a quicker response time? A more effective annealing procedure might be developed and implemented. How much time is required for the atomic voids in a metal to disappear? Is there a more specific range of annealing temperature for aluminum and copper? Is a lower pressure needed within the tube? Tests for positron lifetime in magnetic materials could help to confirm if the magnetic property of the spall of TF does affect the lifetime. It might include testing a metal for lifetimes in its ferromagnetic phase and comparing it to its lifetimes in its paramagnetic phrase (below and above its Curie temperature). Finally, one of the annealed samples of this work, aluminum or copper, could be used as a reference material for subsequent tests on the steel bearings. For example since positron lifetime within aluminum is known at this point then its contribution to the spectrum can be subtracted, leaving only counts associated with decay within the steel. In turn, a more accurate analysis of the spectrum can be performed. 37

47 APPENDIX A The Gluon Fluid Within the atom is often considered a vacuum; that is, the protons, neutrons and electrons are in a space devoid of matter except themselves. However, these particles are no longer considered to be the fundamental particles. After probing deeper within the nucleons physicists have discovered composite particles: quarks and gluons. So according to the Standard Model the fundamental particles are now leptons, quarks, and the particles which mediate forces/interactions between them. The mediators of the fundamental strong force (force carriers) between the nucleons are the gluons. A bunch of gluons is called a gluon field. The mediators of the residual strong force are the mesons, and thus a bunch of mesons make up a meson field. These fields, and especially the gluon field, might exist outside the nucleus and can form a fluid--- a Imagination is more gluon fluid or quantum fluid. important than knowledge. This implies that the electrons, neutrons and protons Albert Einstein are immersed in a fluid made up of gluons--- everywhere--- just as hydrogen, carbon, oxygen, nitrogen, etc. bond together to form the fluid (air) in our classical world. Electrons, neutrons, and protons are thus immersed in a gluon fluid; while soccer balls, ping pong balls and tennis balls are immersed in air. The Quantized Magnus Force affects the aforementioned threesome, and the Classical Magnus Force affects the latter three (see Appendix B). Since the gluons are surrounding all sub-atomic particles including the nucleons that might very well explain why interactions via the strong (nuclear) force are the quickest, compared to interactions via the weak and electromagnetic forces ****. [2] **** Time frames (in seconds) for interactions via three of the four fundamental forces are 10-6, and for Weak, Electromagnetic and Strong respectively. [2] 38

48 APPENDIX B Why does a pps annihilate quicker than an ops? The electron and positron have the proclivity to annihilate within nanoseconds in the case of forming ops or within picoseconds if pps is formed. Why does the ops take a longer time than the pps to annihilate? There are two explanations for this event. One is a semiclassical explanation based on hydrodynamics, while the other is of course the bona fide reason based quantum mechanics. In a soccer game a player takes a corner kick and curves the ball towards the goal. While playing ping pong both players might put so much spin on the ball that it curves in bizarre directions. Likewise in tennis a server can put amazing amount of spin on the ball that it curves in mid-air and even after bouncing. How is this behaviour explained? These are examples of the Magnus Effect (Force). Bernoulli s principle says that for a flowing fluid the pressure is highest where the velocity is lowest and the pressure is lowest The Quantized Magnus Force where the velocity is highest. Now imagine a tennis ball coming out of the page and spinning from right to left (clockwise). The fluid in which the ball is immersed is air, and a thin layer of this air is wrapped around the ball as it spins. Now the velocity of the air flowing into the page and around the left side of the ball will add to the angular velocity of the ball as it comes out of the page (See Figure B-1a). Meanwhile, the velocity of the air Figure B-1b: An anticlockwise-spinning ball in the classical world, which corresponds to the spin-up of a particle in the quantum world. 39 Figure B-1a: A clockwise-spinning ball in the classical world, which corresponds to the spin-down of a particle in the quantum world. flowing into the page and around the right side of the ball will counteract the angular velocity of the ball

49 coming out of the page. In this situation there is a higher pressure along the right side of the ball and there is a lower pressure along the left side (Figure B-1b shows the opposite situation). The result is a net force pushing the ball to the left as it comes towards you (the reader); this is the Magnus Force. Now imagine that for a positronium a fictitious quantized Magnus force can cause the positron and the electron to be sucked into the space separating them during orbit. In an ops formation, the positron and the electron have parallel spin (i.e. both spin-up or spin-down). This means that the velocity of the fluid in the space between the two particles is lower than other places, since their angular velocities partially cancel. In turn, there is an increase in pressure which inhibits the suction force, and collision is delayed (see Figure B-2a). Figure B-2b: With opposite spin, the pressure in-between them is lower. In the other situation, whereby a pps is formed the positron and the electron have antiparallel spin (i.e. one spin-up and the other spin-down, or vice versa). This implies that the velocity of the fluid in the space between the pair is higher than at other places, since the angular velocities add-up. Thus, there is a decrease in pressure (Figure B-2b). In turn, there is a net force which causes the particles to be sucked in and collide; this is why pps s tend to have a shorter lifetime than ops s. The average lifetimes of pps and of ops are 125 ps and 142 ns respectively. The Magnus Effect was first described in classical terms and the equation for the Magnus Force is: 40 Equation B-1 where S is the coefficient of fluid resistance, such as air, across the surface of the object, ω is its angular velocity and v is its linear velocity. Now on the quantum level, ω is related to angular momentum L by: where I is the moment of inertia. Also quantization of angular momentum gives: Figure B-2a: With similar spin, the pressure in-between them is higher. Equation B-2