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micro-electron-volts

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micro-electron-volts

    ADVANCED UNDERGRADUATE LABORATORY

    EXPERIMENT 14, MOS

    The Mössbauer Effect

Last revision: March 2006 by Jason Harlow

    Revised: June 1997 by Joe Vise, 1989 by John Pitre and Derek Manchester

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Introduction

    In this experiment, you will look at energy levels in an atomic system of the order of tens of micro-electron-volts using nuclear gamma rays from that system in the energy range of 14 kilo-electron-volts. The Mössbauer effect makes this possible.

    In 1961 the work of Rudolph L. Mössbauer (see Brown 1963), on resonant absorption of nuclear gamma rays in solids was recognized with the Nobel Prize. His work extended the concept of resonant absorption of light in atomic systems to the nuclear domain and is perhaps most simply understood by analogy with the atomic case.

     Atomic resonance can be noticed very easily by focusing the yellow light emitted by Sodium atoms, the familiar D lines, into a sealed bulb containing Sodium vapour. A faint yellow glow may be observed immediately in the bulb indicating that atoms here strongly absorb energy from the incident beam of yellow light and re-radiate it uniformly in all directions. In other words, incident photons have an energy which is strongly resonant with an allowed energy transition of electrons in the Sodium atoms

    of the bulb.

     Nuclear photons (gamma rays) emitted by one nucleus can similarly be made to resonate with allowed energy transitions in other nuclei. This was first shown by P.B. Moon. It was not until

    Mössbauer's discovery of recoilless emission however, during his graduate studies at Heidelberg in 1957, that such resonant scattering became an extremely accurate and valuable tool in the investigation of diverse problems in physics, chemistry and biology.

     A brief description of the Mössbauer effect is given in the following pages. A clear and much more complete explanation is given by Wertheim. For a treatment of the Mössbauer effect at an advanced level see Harrison pp. 423-427 or the paper by Lipkin which is at the end of this manual. To understand the new idea that Mössbauer brought to bear in the analysis of emission and absorption of gamma rays by atoms in solids, three different situations need to be considered.

    1. When at atom in a solid emits a gamma ray, it recoils. The recoil energy and velocity are simply

    calculated by application of the conservation requirements for energy and momentum.

    2E E (1) ;r22Mc

    where E is the gamma ray energy and M the mass of the recoiling atom. If the recoil energy is

    large compared to the binding energy of the atom in the solid, the atom will be completely

    dislodged from its lattice site.

    2. If the recoil energy is larger than typical energies of lattice vibration but less than the binding

    energy, the atom dissipates the recoil energy by heating the surrounding solid.

    3. If the calculated recoil energy is smaller than phonon energies, it is possible for the atom to emit

    (or absorb) rays without recoiling at all (a result which is properly described only by the

    quantum theory of lattice vibration). This is the Mössbauer effect! This means that gamma

    rays whose frequencies are not spread over a wide range by Doppler (recoil) motion of the

    emitting (or absorbing) nuclei can be obtained. That is, the gamma rays all have precisely the

    same frequency in the lab frame and the line-width of the emitted radiation is extremely small in

    this case. In fact this radiation has a line-width much narrower than typical line-widths of

    hyperfine electronic levels and shifts in atoms. Consequently, if the frequency of the gamma

    radiation (in the lab frame) can be varied in some controlled fashion about the energy of

    unknown energy states in sample nuclei nearly in resonance with the gamma rays, high

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    resolution spectroscopy can be performed. The unknown energy states and the local environment

    of sample nuclei can be probed.

    Fortunately it is a simple matter to change the frequency of narrow line-width gamma radiation. By varying the velocity of the source relative to the sample, the gamma ray frequency in the laboratory reference frame can be tuned by the well-known Doppler effect. This tuning has permitted Mössbauer measurement of isomer shifts, nuclear moments (i.e. spin, magnetic dipole and electric quadrupole moments), crystal fields and magnetic hyperfine structure. It has also been used for non-destructive analysis of the chemical composition of substances and the measurement of lifetimes of highly-ionized electronic states in solids.

The Source 575757The radioactive material which constitutes the source is Co in Rhodium. Co decays to Fe by

    electron capture according to the diagram in Figure 1.

     5757Figure 1. The decay of Co to Fe. (E.C. denotes electron capture.)

     57The nuclear levels of Fe in the Rhodium are unsplit and the line-width of the 14.4 keV gamma ray is small compared to the energy of interaction of the nuclear magnetic dipole moment of 57Fe with its own internal field in the absorber. 57 At the site of the Co in the host material of the source there must be either no magnetic field or else the electron spin correlation time must be very short. To say that the electron spin correlation time is short means that the field is changing rapidly enough that the average field may be taken to be zero. In 57either case there will be no hyperfine splitting of the Fe daughter. The crystal structure of the host must

    be cubic so that there is no quadrupole splitting. By experiment, Rhodium has been found to be the host 57with these properties which gives the narrowest lines. Also, the concentration of Fe in the source must

    be small enough that there will only be long range, and hence weak, Fe-Fe interactions.

Magnetic Splitting in the Absorber

    The source emits a monochromatic line which may be Doppler-tuned to absorption resonances of 57Fe in the sample foil. Since Fe is cubic there is no quadrupole splitting in the absorber. The resonances 57are due to magnetic splitting of the Fe nuclear levels which arise from the interaction of the nuclear 57magnetic dipole moment with the magnetic field due to the atoms own electrons. For Fe, I = ? in the

    ground state and I = 3/2 for the excited state (I = nuclear spin) which gives rise to the 14.4 keV gamma

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    ray. Each state is split into 2I + 1 magnetic sublevels (see Figure 2) and allowed transitions must satisfy m = 0, ?1. The energy difference between magnetic sublevels is E = B where µ is a nuclear NN

    magneton and where the g factor is different for different levels. For a derivation of this equation and an explanation of g factors and magnetic moments, see appendix I.

    Figure 2. Magnetic splitting of nuclear levels. (Nuclear Zeeman Effect).

    With this condition only six transitions are possible. For an unmagnetized absorber with a single line source, the ratio of the intensities for absorption is 3:2:1 as is shown schematically in Figure 2 (see also Wertheim p. 75).

     57Figure 3. Reference splittings for calibration of Fe, given in terms of the velocity required to Doppler

    shift a 14.4 keV X-ray (mm/s) to the appropriate energy to produce a transition.

    The internal field has been measured by Preston et. al. And it produces splittings which give rise to Mössbauer lines shown schematically in Figure 3. The data was taken at 294 K and the separations of the lines which are given in mm/s have uncertainties of ?0.025 mm/s.

Isomer Shift

    The nucleus in an atom is always surrounded and penetrated by the electronic charge with which it interacts electrostatically. This interaction shifts the nuclear levels and the shift is different for ground and excited states. The electron charge density at the nucleus is an atomic or chemical parameter since it is affected by the valence state of the atom. Thus shifts of the nuclear levels will be different in the absorber and the source since the surroundings of the Fe nucleus are different. This shift of levels is shown in Figure 4 and the difference E ? E is the isomer shift. sa

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    Figure 4. Schematic diagram of the isomer shift in a source and absorber.

    Since isomer shifts result from differences between two levels, one substance must be taken as a standard and other substances are measured relative to it. Figure 5 shows isomeric shifts in mm/s relative to Iron.

    By convention, velocity is defined as positive for approaching relative motion between source and observer. Thus the source with the more negative shift has the larger nucleon energy level difference and hence the smaller electron density at the nucleus.

    Figure 5. Isomeric shift (mm/s) relative to metallic iron.

Lifetime of States

    The Doppler shifted frequency, to first order for a moving source is given by

    ?';1 (2) ?c~?

Thus, , the line width, ( = E = hν) of the excited state of Iron is given by:

     (3) EE;c

where µ is the full width at half maximum in velocity units.

    From the uncertainty principle, the line width E and the lifetime, , are related by

     ?, = ħ (4)

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In this experiment the observed line width, Γ’, is actually twice the real line width, , since the

    Mössbauer spectrum incorporates a convolution of the source and absorber line width. Thus

    2; (5) ;(

     ( is obtained from the full width at half maximum of the Mössbauer spectrum in velocity units where

    and equation (3). ?7 The accepted value of = 1.4 × 10 is an upper limit and your value probably will be smaller.

    Why?

Experimental

    In the method used here, a spectrum is obtained of the number of counts per second, as a function of the velocity of the source, of 14.4 keV gamma rays that have passed through the absorber into a detector. The detector is a proportional counter which is efficient to the detection of this energy of gamma ray and is inefficient to the detection of higher energy gamma rays. To achieve this spectrum, 57the Co source is moved forward and back with a velocity, linearly varying as a function of time, and then multi-channel scaling is performed on the pulses (counts) coming from the detector. This produces a series of folded count versus time spectra from which counts versus velocity can be deduced.

    SpectroscopyPreAmpProportionalPulseGain=x1CounterAmplifier

    Fastscope

    2000 VPowerSupplySCAinputEG+GMCS plusMCS cardStartinput

    FrequencyCounter

    TTLDelayExtoutputBoxWavetektriggerSlowfunctionscopegeneratorvelocityySignalpick-offinputoutputMossbauerDriverMUT

    Mossbauer

    Transducer

    Figure 6. Schematic diagram of connections to the apparatus.

    In multi-channel scaling, a number of bins or channels, each representing a time Δt, called the

    “dwell time”, record the counts as they come in. A “start” pulse starts the counting and if a pulse arrives,

    a count gets added to that bin that corresponds to the time delay for that pulse. (For example, if we set

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    the dwell time to be 100 μs, and if a counter pulse arrives 20 ms after the start pulse, then one more count will be added to the “Channel 200” bin.)

    The circuit hook-up for the apparatus is shown schematically in Figure 6 and a schematic section of the transducer is shown in Figure 7. Figure 8 illustrates the folded count versus time spectra.

    Figure 7. Schematic out view of the transducer.

    The source is mounted on the Mössbauer transducer which produces a velocity of motion proportional to the voltage from the Wavetek function generator. A slow, highly linear, triangular signal is produced by the Wavetek. The stationary absorber is a thin Fe foil. At liquid nitrogen temperatures there would be predominantly recoilless absorption but even at room temperature about half the 57absorption events in Fe are recoilless and a reasonable spectrum can be obtained.

    counts

    time

    velocitytime

    Figure 8. Folded “time” spectrum and associated velocity-time graph.

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The Detector System

     The detector is a gas proportional counter and information on its operation may be obtained from appendix II and references such as Brown (brief) and Snell (more extensive). The detector voltage, which should be between +1900 V and +2300 V, should be applied slowly in steps. Higher voltages are required as the detector ages. One wishes to keep the detector voltage as low as possible since this increases the detector lifetime. A compromise must be made since in order to have good signal to noise for this experiment one must be able to isolate the 14.4 keV peak from the other features. 57As indicated in Figure 1, the Co source emits gamma-rays of energies 137 keV, 123 keV and

    14.4 keV. As you will observe, other energy photons also reach the detector. These include atomic X-5757rays from Fe which has been left in an excited state following the Co decay. Also (atomic) X-ray

    fluorescence from materials in the region of the detector or source is picked up in the detector. We recommend that you look up the characteristic X-ray energies. Table 1 is a guide to the photon energies that you might expect to find.

    Photon Energy (keV) Material Origin of Radiation 57137, 123, 14.4 Co Nuclear gamma-rays following EC decay 577.1, 6.4 Fe K X-rays from excited daughter of 57Co

    86, 73 Pb K X-rays from X-ray fluorescence

    15, 13, 10.5 Pb L X-rays from X-ray fluorescence

    ~3 Pb M X-rays from X-ray fluorescence

    23, 20 Rh K X-rays from X-ray fluorescence

    2.9, 2.7 Rh L X-rays from X-ray fluorescence

    1.5 Al K X-rays from X-ray fluorescence

    Table 1. Photon sources near the proportional counter with energies.

     57The shape of the broad spectrum for the Fe source is shown in Figure 9. The 123 keV and 137

    keV peaks are not seen because of the decreased detector sensitivity at these energies, but they do produce effects which are detectable, such as Compton scattering and fluorescent X-rays from surrounding materials and the accompanying Krypton escape peaks that are associated with all X-rays of 57sufficient energy. Figure 10 shows the Fe spectrum for an increased detector and amplifier gain.

    Figure 9. X-ray spectrum for low detector voltage and low amplifier gain.

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    Figure 10. X-ray spectrum for high detector voltage and high amplifier gain.

    In order to not have the Mössbauer absorption overwhelmed by detection of non-resonant radiation energies, it is necessary to have the detector register only the 14.4 keV gamma-rays and not count those of other energy. (You might reflect on why all lead shielding in the apparatus is lined with aluminium.) The discrimination against unwanted photons uses the property of the detector that the pulses out of the proportional counter have heights (voltages) proportional to the photon energy. Moreover, the multi-channel scaler (MCS) has, at its front end, a single channel analyzer which accepts only a certain range of pulse heights.

    To set up the detector to select only the 14.4 keV gamma-rays:

    1. The detector should feed the pre-amplifier and then the amplifier. Start with a pre-amp gain

    of “×1” and an amplifier gain of about 1.0×30. (Use 1μs amplifier pulse shaping and

    unipolar pulse output.) Using the fast pulse (60 or 100 MHz) oscilloscope connected to the

    amplifier output, raise the high voltage until the largest pulses reach about 7 Volts. These

    largest pulses are from the 137 keV gamma-rays. The pulses you are interested in, from the

    14.4 keV gamma-rays, are the intense traces about 1/10 of the voltage of the highest ones. If

    you raise the amplifier gain by a factor of about 3 to 5 times what you had, this will increase

    the height of the pulses out of the amplifier by the same factor so that you will see these 14.4

    keV pulses more clearly.

    2. Connect the amplifier output to the MCS input. (For operation of the MCS, including setting

    up you own directory, see Appendix III.) You will now take a pulse height spectrum to

    enable you to set the MCS to respond to only pulses of height which correspond to the 14.4

    keV gamma-ray energy. With your original amplifier gain setting (pre-amp gain of “×1” and

    amplifier gain of about 1.0×30) and the MCS in operation, start colle3cting a pulse height

    spectrum by clicking on Acquire ? SCA Sweep. The display on the screen is a histogram of

    the distribution of pulse heights that you previously saw on the oscilloscope. You should be

    able to identify a number of the higher energy photons mentioned in Table 1. The 14.4 keV

    gamma-ray may or may not be visible it may be at too low a voltage. Now raise the

    amplifier gain as you did in step 1 above. The voltage position of all the peaks will move up

    by the factor by which you raised the gain. This should help you identify the 14.4 keV

    gamma line. You now set the “window” of the single channel analyzer (SCA) by dragging

    the mouse across the part of the spectrum you want to select. Be sure to include the whole

    peak and no more. (Note that the peak is broad as gas proportional counters have poor

    energy resolution.) Now click on Set SCE. If you want to check on the Voltage range you

    have selected, you can find it (and change it) by clicking on Acquire ? Input Control on the

    main screen.

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The Transducer

    The Mössbauer transducer, shown in Figure 7, provides a controlled motion of the source. It has two coils mounted to a common shaft which moves longitudinally. The coils sit in magnetic fields so that the field cuts the wires normally. The drive coil moves the shaft, providing a force proportional to the current through it. The pickup coil produces a voltage proportional to the velocity of the shaft. The Mössbauer Driver with the transducer is represented schematically in Figure 11.

    PickupDriveSourcecoilcoil

    WavetekfunctionFunctioninputDifferenceGeneratorAmplifier

    Velocity

    pick-off

    (to scope)

    Figure 11. Functional schematic diagram of the Mössbauer driver and transducer

    The pickup coil output voltage is subtracted from the Function Input (derived from the Wavetek

    function generator) and then amplified. The amplified output is used to drive the drive coil. If the amplifier has sufficient gain, the feedback in this arrangement drives the shaft so as to make the pickup coil voltage follow the Function Input voltage. Thus the velocity of the shaft is proportional to the

    Function Input voltage. There are other features in the circuitry that help prevent the transducer shaft from wandering off too far past the ends of normal motion. The Velocity Pickoff enables you to display

    an actual velocity-time graph on the slow cathode ray oscilloscope.

Velocity Selection of the Source

    The internal magnetic field in the absorber produces the magnetic splitting of the nuclear levels and the transitions between the levels have energies which differ from the energy of the X-rays from the source. These energy differences are given in Figure 3 in terms of the velocity required to Doppler shift a 14.4 keV X-ray from the source to the appropriate energy to produce a transition. From Figure 3 it can be seen that the velocity must range from about ?6 mm/s to +6 mm/s in order to see all the lines.

    The maximum velocity of the source is determined by the amplitude control on the Wavetek generator. If, for a given velocity, the period is large, then the amplitude of the transducer must be correspondingly large. If the amplitude is too large then the transducer will be overdriven and this will give rise to glitches in the velocity profile as seen on the oscilloscope. On the other hand, if the amplitude is small, the period will have to be short in order to give high enough velocities to perform this experiment. This will make visual observations of the amplitude using a travelling microscope very difficult. A reasonable compromise for the amplitude of the transducer is between 0.5 and 1 mm.

    A quick approximation to the amplitude of the source should be made using the dial gauge. A rough approximation to the period may be taken from the oscilloscope or from the counter. Since the velocity changes linearly with time, then v may be calculated from where v;2v. d;vtmaxmax

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