Download mössbauer spectroscopy

MÖSSBAUER SPECTROSCOPY
AIM
The aim of this experiment is to introduce the student to the methods in Mössbauer Spectroscopy —
recording and analysis of Mössbauer spectra in the resonance absorption mode, and to evaluate
nuclear and solid state parameters.
INTRODUCTION
When an atom in an excited state makes a transition to the ground state, the resulting radiation may
be absorbed by atoms of the same kind thereby raising them into the excited state. This process is
known as resonant absorption and is a familiar feature of optical spectroscopy. For instance, the D
lines of sodium are strongly absorbed by sodium vapour.
∆E
{
hν = E - R
E
hν = E + R
Emission
Absorption
hν = E – R
hν = E + R
Fig. 1
Effect of recoil on emission and absorption
In the case of gamma radiation from nuclei, however, resonant absorption does not usually take
place because of the relatively large momentum associated with gamma ray photons. When a
stationary nucleus of excitation energy E emits radiation in a transition to its ground state, the
nucleus recoils so as to conserve linear momentum and the energy of the gamma ray is less than E
by the recoil energy R which is approximately E2/2Mc2, where M is the nuclear mass. Similarly, if a
stationary nucleus is to be excited by an energy E due to the absorption of radiation, (see Fig. 1) the
photon energy must be approximately E + (E2/2Mc2) for momentum to be conserved. Thus the
centres of the absorption and emission lines are displaced relative to one another by an energy
separation E2/Mc2 and if this is much greater than the line width, resonant absorption will not be
observed (See Fig. 2). In optical spectra, E is small enough for the effects of recoil to be negligible,
but for a 100 keV gamma ray from a nucleus of mass number 50, E2/Mc2 is roughly 0.2 eV, larger
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than the natural widths of most gamma rays and also larger than the Doppler width of such a 100
keV line at room temperature.
Fig 2.
Condition for resonance fluorescence of gamma radiation
(a) represents emission and absorption lines overlapping considerably
(2R ≤ Γ) so that the resonant experiment can be achieved, whereas in
case
(b) 2R > Γ, no resonant absorption can occur
In 1958, Mössbauer demonstrated that if the emitting and absorbing nuclei are strongly bound in
crystalline solids, strong resonant emission and absorption of gamma rays may occur. In order to
observe the resonance absorption, gamma ray energy is changed over a small range employing
Doppler motion. If the source and absorber are stationary and nuclei of the source and absorber are
in the same environment, resonance absorption and re-emission take place. When either the source
or absorber is moving, the spectrum of the gamma radiation undergoes a Doppler energy shift ∆E ,
which is given by
∆E =
V
E
c
Where E is the energy of the emitted gamma ray, c is the velocity of light and V is the relative
velocity of the source and absorber.
Subject to certain approximations, the physical phenomena such as line width and mean lifetime of
the emitting nucleus, internal magnetic field in ferromagnetic material and the magnetic moment of
the first excited state of
57
Fe can be measured, and the energy resolution of the Mössbauer
spectrometer can be determined.
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DESCRIPTION OF THE EXPERIMENT
A block diagram of the experimental set-up is shown in Fig. 3.
SOURCE
H. T.
PREAMP
DRIVE
DETECTOR
V
ABSORBER
MCA COMPUTER
CARD
(PHA/MCS & SCA)
AMP
Fig. 3
START
CHAN.
ADV.
MÖSSBAUER
DRIVING UNIT
(FUNCTION GEN.)
Mössbauer set-up
+V
t
-V
T
Fig. 4
Function generator waveform
The Mössbauer source is mounted on a drive, which could be moved with a continuously varying
velocity between zero and a preset value. The variation is made cyclically by using a function
generator which generate a triangular waveform, as shown in Fig. 4 (constant acceleration mode).
The velocity of the drive changes from -V to +V in a half cycle (T/2 seconds). The analogue output
from the function generator is applied to a power amplifier, which drives the source. The output
from the function generator is also applied to the MCA (Multichannel Analyzer) to provide
synchronization and channel advance in multichannel scaling. A correspondence is established
between the channel numbers and the velocity of the drive (consequently to the gamma energy
through the Doppler equation).
Gamma rays emitted by the source pass through an absorber and the transmitted gamma rays are
detected by a radiation detector (proportional counter). The output of the detector, after
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amplification, is applied to a single channel analyzer, the window of which is set to pass through it,
the amplified output corresponding to the Mössbauer transition energy. The logic pulses from SCA
(Single Channel Analyzer) are applied to the signal input of the MCA and counted at the appropriate
velocity (energy). A Mössbauer spectrum is thus a Plot of the transmitted gamma rays through an
absorber versus velocity of the source (Doppler shifted gamma energy).
57
Co
271d
7−
2
EC
5−
2
136 keV
91%
9%
3−
2
14.4 keV
1−
2
0
Mössbauer
gamma ray
57
Fe
Fig. 5
57
Nuclear decay scheme of Co showing the transition
giving the 14.4 keV Mössbauer gamma ray
The 14.4 keV gamma ray in 57Fe is the most convenient transition for Mössbauer spectroscopy and
57
Co source populates it in its decay. The decay scheme of the radioactive isotope 57Co is shown in
Fig. 5. The Mössbauer source consists of 57Co embedded in a copper lattice. This is rigidly mounted
on the drive.
If a stainless steel foil is used as the absorber, the Mössbauer spectrum shows a single absorption
dip, since no magnetic fields act on 57Fe nuclei in the absorber. The position of the absorption dip,
however, is displaced from V = 0, ( E γ = E 0γ ) as the electronic charge densities ψ(0)2 at the 57Fe
nuclei in the source and the absorber are different. The shift δ is the result of electric monopole
interaction and is referred to as the "isomer shift". It is given by
δ =
[
Ze 2
R e2 − R g2
10 ε 0
][ ψ(0) 2A
2
− ψ(0) S
]
where Z is the atomic number (Z = 26), ε 0 is the permittivity. R e and R g are the nuclear radii of 57Fe in
the excited ground states respectively.
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If a natural Fe foil is used as an absorber the levels between which the Mössbauer transition occurs
are split up due to the magnetic dipole interaction. The 14.4 keV level is split up into four
components and the ground state is split up into two components. Considering the selection rules
for this predominantly magnetic dipole transition (∆m = ±1, 0), the absorption line is split up into six
components as illustrated in Fig. 6.
mI
+3/2
+1/2
I
-1/2
3
2
counts
-3/2
velocity
-1/2
1
2
Fig. 6
+1/2
57
The effect of magnetic splitting on the nuclear energy levels of Fe, showing the
Mössbauer absorption transitions and the resulting spectrum in the absence of
quadrupole splitting. The overall splitting of the lines in the spectrum is
proportional to the total magnetic field at the nucleus
The energy E II' corresponding to the different lines is given by the relation


 g' 
 m I' 
E II' = E 0 + gµ N B  m I − 
g




Where E 0 = 14.4 keV, g and g’ are the g factors for the ground and excited states respectively, m I
and m I' are the magnetic quantum numbers of the ground and excited states, µ N is the nuclear
magneton and B is the hyperfine magnetic field acting on the 57Fe nucleus (in the absorber).
The lines separations ( ∆E 1,2 = ∆E 2,3 = ∆E 4,5 = ∆E 5,6 = g' µ N B) yield the magnetic splitting
energy of the excited state.
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If a non-ferromagnetic Fe compound is used as the absorber and
57
Fe nuclei are located in an
environment that has a surrounding asymmetric electric charge distribution, an electric field
gradient (EFG) acts on 57Fe nuclei. The energy levels in this cases are split up due to the electric
quadrupole interaction. In 57Fe this interaction splits the excited state into two components, while
the ground state (spin 1/2) is not split up (because of vanishing Quadrupole moment) as shown in
Fig. 7.
mI
± 3/2
I
± 1/2
counts
counts
3
2
δ
δ
∆
0
0
velocity
velocity
± 1/2
1
2
(a)
(b)
57
Fig. 7 The effects on the nuclear energy levels of Fe of (a) the isomer shift and (b) the
quadrupole splitting. The Mössbauer absorption transitions and the resulting
spectra, which give the isomer shift δ and the quadrupole splitting ∆, are also
shown
The resulting Mössbauer spectrum has two absorption dips, the separation between them ∆E Q’
being given by
∆E Q' =
eQ δ 2 U
2 δZ 2
Where Q is the Quadrupole moment of the
3
δ 2U
state and
is the EFG acting on 57Fe nuclei.
2
2
δZ
EXPERIMENTAL PROCEDURES
Note: Do not adjust the parameters on any of the modules in the set-up
1)
Calibration of the Mössbauer spectrometer and determination of nuclear parameters g' and
T 1/2 .
a)
Follow the data acquisition procedures in the appendix to collect the pulse height
spectrum of the 57Co source as shown in fig. 8.
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COUNTS
14.4 keV
511
0
CHANNEL NUMBER
SCA window
width
Fig. 8
b)
Spectrum of
57
Co
Place a thin natural Fe foil (0.028 mm) between the source and the detector and observe
the pulse height spectrum again.
c)
Locate the line corresponding to the 14.4 keV transition. Refer to the operating procedures
in the appendix and set the window width (Lower level discriminator LLD & Upper level
discriminator ULD) of the Single Channel Analyzer (SCA) for this energy level.
d)
Start acquiring the Mössbauer spectrum for a duration of at least 6 to 8 hours.
Note: The spectrum has two sets of 6 lines. They arise due to the
velocities in the range -V to +V occurring twice in each cycle.
e)
Determine centroid channel of each line ∑ N I C I ∑ N I where N I are the counts and C I
are the corresponding channel numbers. Determine the channel corresponding to V = 0
(which is the centroid of the total distribution in each half cycle). This is obtained as the
average of the three symmetric sets of lines in each spectrum. Calibrate the velocity scales,
using the standard data for natural Fe foil.
∆V(1,6) = 10.657 mm/sec
∆V(2,5) = 6.167 mm/sec
∆V(3,4) = 1.677 mm/sec
Also calibrate the energy scale, using the relation
∆E = E 0γ ∆V / c
with E 0γ = 14.41425 keV
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f)
Determine the line width Γ (FWHM) by averaging the values of all the peaks in energy
units. Evaluate the half-life of the 14.4 keV state using the relation:
T1
2
= (n 2) / Γ
Compare it with the experimental value 98.4 ns.
g)
Determine the average value of the line separation (∆E ij ) and use it to calculate the g'
factor of the 14.4 keV state assuming B = ~33 T.
∆E ij = g' µ N B
where µ N = 3.152 x 10-8 eV/T is the nuclear magneton. Compare your values of g’ with the
standard value which is -0.102.
h)
Repeat the experiment with stainless steel (0.0254 mm) absorber and determine the
isomer shift.
i)
Compare the different values of isomer shifts and comment.
OPTIONAL
2)
Determine hyperfine magnetic field
a)
Repeat the experiment with Fe 2 O 3 (20 mg/cm2) absorber.
b)
Calculate the hyperfine magnetic field B from the line separations in Fe 2 O 3 , assuming g'
determined in the previous experiment (or the known value).
REFERENCES
1)
Hans Frauenfelder, The Mössbauer Effect, W.A. Benjamin Inc. Publisher (1963).
2)
Leopold May, An Introduction To Mössbauer Spectroscopy, Plenum Press (1971).
3)
V.G. Bhide, Mössbauer Effect and Its Applications. McGraw Hill (1973).
4)
Richard L.Cohen, Aplications of Mössbauer Spectroscopy, Vol 1, Academic Press (1976).
Mossbauer Spectroscopy-revised 2009.doc
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Appendix
MOSSBAUER EXPERIMENT DATA ACQUISITION PROCEDURES
1. GETTING STARTED
Double click Gamma Acquisition icon
Pull down FILE menu
Click Open Datasource
Check Detector button
Select Mossbauer followed by the Open button
2. DATA ACQUISITION
A. Pulse Height Analyzer Mode (PHA)
Pull down MCA menu
Click Acquire Setup
Enter Sweep Count value as 1,000,000
Click Adjust
Check the following default setting:
a) Dwell Range: external
b) Dwell value: 1000
c) Scan window: 2.00 %
Check PHA button under Disc. Mode
Do not exit “Adjust” window at this point of time
Start acquiring the pulse height spectrum by clicking START tab
Stop acquisition by clicking STOP tab
Go to FILE menu to save or data plot the spectrum
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B. Multichannel Scaling Mode (MCS)
Identify the 14.4 keV peak on the pulse height spectrum
Place the cursor at the valley position before the 14.4 keV peak
Press the Ctrl & L keys simultaneously to set the left marker. This corresponds to the SCA LLD.
Next place the cursor at the valley position after the 14.4 keV peak.
Press the Ctrl & R keys simultaneously to set the right marker. This corresponds to the SCA ULD.
Under the Adjust window, check ROI button
Click NEXT tab
Click SET tab under Set ROI
Exit Adjust window
Clear the pulse height spectrum
Pull down the MCA menu and click Acquire Setup
Change Sweep Count value to 0
Click Start tab to start acquisition of the Mossbauer Spectrum
3. TO PRINT DATA REPORT FOR ACQUIRED SPECTRUM
Go to Analyze Menu
Click Execute Sequence followed by Spectral Data Request.
Click Maximize the Report Window icon
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