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RESEARCH ARTICLE
|
NOVEMBER 10 2023
A miniaturized piezoelectric Mössbauer spectrometer with
feedback control
P. Guzman
;
C. M. Quine
;
S. H. Lohaus
;
L. Schul
;
R. Toda
;
V. J. Scott
;
B. Fultz
Rev
. Sci. Instrum.
94, 115107 (2023)
https://doi.org/10.1063/5.0157651
14 November 2023 23:36:47
Review of
Scientific Instruments
ARTICLE
pubs.aip.org/aip/rsi
A miniaturized piezoelectric Mössbauer
spectrometer with feedback control
Cite as: Rev. Sci. Instrum.
94
, 115107 (2023); doi: 10.1063/5.0157651
Submitted: 9 May 2023
•
Accepted: 19 October 2023
•
Published Online: 10 November 2023
P. Guzman,
1, a)
C. M. Quine,
1
S. H. Lohaus,
1
L. Schul,
1
R. Toda,
2
V. J. Scott,
2
and B. Fultz
1
AFFILIATIONS
1
California Institute of Technology, Pasadena, California 91125, USA
2
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91108, USA
a)
Author to whom correspondence should be addressed:
pgguzman@caltech.edu
ABSTRACT
A Mössbauer spectrometer was built and evaluated using an amplified piezoelectric actuator under feedback control for the Doppler velocity
drive. The actuator was driven with a quadratic displacement waveform, giving a linear velocity profile. The optimization of the piezoelectric
Doppler drive under feedback control was performed with measurements from a laser Doppler vibrometer.
57
Fe Mössbauer spectra of
α
-iron
in transmission geometry show minimal peak distortions. The performance of this piezoelectric Doppler drive makes Mössbauer spectrometry
possible in applications requiring small size, mass, and low cost.
Published under an exclusive license by AIP Publishing.
https://doi.org/10.1063/5.0157651
I. INTRODUCTION
Mössbauer spectrometry is a robust technique that provides
quantitative information about the structural, electronic, and mag-
netic properties of materials containing nuclear resonant isotopes,
such as
57
Fe,
119
Sn,
121
Sb,
151
Eu, and
191
Ir. The “Mössbauer effect”
is based on the recoil-free emission and absorption of
γ
-rays in
solids, allowing for the energy of the outgoing
γ
-ray to be accurate
to 10
−
9
eV.
1
Mössbauer spectra provide quantifiable information
on the interactions between the nucleus and its neighboring elec-
trons, which cause small perturbations to the nuclear energy levels
known as “hyperfine interactions.” The energies of the
γ
-rays are
tuned by moving the radiation source with a velocity,
v
, relative to
the sample. This gives a Doppler shift
Δ
E
=
(
v
/
c
)
×
E
0
, where
E
0
is
the energy of the
γ
-ray,
∼
14.41 keV for
57
Fe. This
Δ
E
is cyclically
scanned when acquiring a Mössbauer spectrum. A velocity range of
±
10 mm/s is sufficient to scan through many spectra of nuclear res-
onances for
57
Fe Mössbauer spectroscopy; however, in some cases,
higher velocities are needed.
1–4
The main components of a standard Mössbauer spectrometer
are an electromagnetic Doppler velocity drive, a source of
γ
-rays,
and a photon detector.
1,4,5
A
57
Fe Mössbauer spectrum is a plot of the
intensity of detected 14.41-keV
γ
-ray photons vs Doppler velocity,
v
. The velocity transducer is a key element in a Mössbauer spec-
trometer since the quality of the spectrum is governed by the precise
movement of the radiation source.
Miniaturized electromagnetic Doppler velocity drives have
been developed in the recent past for Mössbauer experiments on the
surface of Mars.
6,7
Notably, MIMOS II was a miniature Mössbauer
spectrometer built for missions on the Mars Exploration Rovers,
Spirit and Opportunity. The MIMOS II spectrometer collected sev-
eral Mössbauer spectra of rocks on Mars, and some spectra showed
a significant amount of iron oxyhydroxide, goethite (
α
-FeOOH).
At the time, this was the best mineralogical evidence for the pres-
ence of water on Mars since goethite is formed only in an aqueous
environment.
8–10
Compared to a miniature electromagnetic Doppler velocity
drive, a piezoelectric actuator as a Doppler drive could significantly
reduce the size, mass, and power requirements of a Mössbauer
spectrometer, making Mössbauer spectrometry available for appli-
cations where miniaturization is essential. Previous publications
report the use of piezoelectric actuators as Doppler velocity drives
for Mössbauer spectrometry.
11–15
None, however, were operated
with feedback control. Here, we report the use of a mechanically
amplified, piezoelectric actuator as a Doppler velocity drive, both in
open loop and in feedback-controlled configurations. Feedback con-
trol overcomes problems with thermal sensitivity of the piezoelectric
material and successfully corrects for nonlinearities and parasitic
oscillations in the dynamics of the drive. The system performance
is nearly comparable to laboratory-based electromagnetic Doppler
velocity drives.
Rev. Sci. Instrum.
94
, 115107 (2023); doi: 10.1063/5.0157651
94
, 115107-1
Published under an exclusive license by AIP Publishing
14 November 2023 23:36:47
Review of
Scientific Instruments
ARTICLE
pubs.aip.org/aip/rsi
II. EXPERIMENTAL
A. Spectrometer configuration
Figure 1 shows a Mössbauer spectrometer with a piezoelectric
Doppler velocity drive arranged in transmission geometry, where
the distance between the source and the sample is 2 cm and the
distance from the sample to the detector is 1 cm. This spectrom-
eter includes a
57
Co source of
γ
-rays (Ritverc MCo7.162), with an
approximate activity of 2 mCi at the time of measurements, mounted
on a mechanically amplified piezoelectric actuator (Cedrat Tech-
nologies APA1000L), a 30
μ
m thick 99.99
+
% purity
α
-iron foil as
the absorbing sample, and a solid state detector (Ketek VITUS H50).
A pair of 350
Ω
resistive strain gauges are used to monitor the
displacement of the transducer and perform feedback control. The
strain gauges have a T-Rosette design and are mounted directly on
the multilayer actuator (MLA) by Cedrat Technologies. The strain
gauges are designed to be compatible with the Cedrat Technologies
piezoelectric controller (CCBu20).
The piezoelectric actuator with the
γ
-source undergoes cyclic
displacements that follow a periodic reference waveform. Typically,
Mössbauer spectrometers are operated in constant-acceleration
mode, where the velocity follows a triangle wave. This linear veloc-
ity profile allows for evenly spaced velocity steps, and each time
step corresponds to a channel in a multichannel scaler. A triangu-
lar velocity profile requires a quadratic displacement profile as the
driving waveform for a piezoelectric Doppler velocity drive. The
57
Fe Mössbauer spectrum of
α
-iron contains six absorption lines
due to the nuclear Zeeman effect.
1,16
For each oscillation period, the
Doppler shifted velocity passes through zero twice (at the turning
points), giving two sets of six absorption lines as shown in Fig. 3. A
microcontroller (Teensy 4.0) is used to generate a reference driving
waveform with a lookup table. This reference waveform is input into
the piezoelectric controller (CCBu20), which compares the feedback
from the strain gauges with the reference waveform and amplifies
the signal to ultimately drive the piezoelectric actuator. In addition,
the microcontroller functions as a 2048-channel multichannel scaler
for acquiring the spectrum over many cycles of the Doppler drive.
The electronics in the experimental setup allow for the deter-
mination of gamma energies with a sample-and-hold analog circuit
combined with a voltage comparator for pulse detection. The micro-
controller uses a 12-bit ADC for binning of the analog values.
FIG. 1.
Spectrometer in transmission geometry. Radiation source is attached to
mechanically amplified piezoelectric actuator with velocity perpendicular to the thin
sample absorber.
FIG. 2.
Energy spectrum resulting from the pulse-height-analysis (PHA) binning
from the piezoelectric Mössbauer spectrometer.
Figure 2 shows an energy spectrum collected with the microcon-
troller, where the pulses from the detector are sorted by their
amplitude (energy binning). The software allows for user-inputted
values to set the discriminator window, which is tested after each
pulse is detected. The pulses in the window around 14.4 keV are then
binned against velocity to obtain a Mössbauer spectrum.
B. Feedback control and low-pass filtering
57
Fe Mössbauer spectra collected without feedback control (i.e.,
open loop) were of poor quality, as shown in Fig. 3. For a high-
performance spectrometer, feedback control of the piezoelectric
actuator is required. The purpose of the PID controller is to dimin-
ish the error
e
(
t
)
between the strain gauge displacement signal
y
(
t
)
and the reference waveform
r
(
t
)
by adjusting the proportional (P),
integral (I), and derivative (D) terms to generate a corrected drive
signal,
d
(
t
)
. The error is defined as
e
(
t
)
=
r
(
t
)
−
y
(
t
)
.
(1)
A digital PID controller operates with discrete time intervals.
17
The CCBu20 controller provides digital PID control and a digital
stabilizing filtering cell, in which ADC and DAC converters are used
to sample the analog signals and perform feedback control digitally.
The sampling time of the digitization process,
T
, determines the dis-
crete time events
t
=
nT
(where
n
=
0, 1, 2,
...
). The adjustment on
the drive signal
d
(
t
)
by the proportional term is
d
P
(
t
)
=
k
P
e
(
nT
)
,
(2)
providing direct amplification by the proportional gain
k
P
. The
adjustment on the drive signal by the integral term is
d
I
(
t
)
=
T
T
I
n
∑
m
=
1
e
(
mT
)
,
(3)
where
T
I
is the integration time. Over time, the integral term min-
imizes deviation from the average reference value. The adjustment
on the drive signal by the derivative term is
d
D
(
t
)
=
T
D
e
(
nT
)
−
e
((
n
−
1
)
T
)
T
,
(4)
Rev. Sci. Instrum.
94
, 115107 (2023); doi: 10.1063/5.0157651
94
, 115107-2
Published under an exclusive license by AIP Publishing
14 November 2023 23:36:47
Review of
Scientific Instruments
ARTICLE
pubs.aip.org/aip/rsi
FIG. 3.
Open loop performance. Velocity error signal
e
(
t
)
, measured LDV velocity profile
y
(
t
)
, and reference velocity profile
r
(
t
)
at a driving frequency of 10 Hz. The
measured LDV velocity profile
y
(
t
)
and the reference velocity profile
r
(
t
)
were offset from zero voltage. (Inset)
57
Fe Mössbauer measurements of a 30
μ
m
α
-iron foil
collected at a driving frequency of 10 Hz in open loop.
where
T
D
is the derivative time constant. The derivative term
impacts the stability properties of the feedback control by prevent-
ing overshoot. The overall adjustment on the drive signal by all three
components is
17–19
d
PID
(
t
)
=
k
P
[
e
(
nT
)
+
T
T
I
n
∑
m
=
1
e
(
mT
)
+
T
D
T
[
e
(
nT
)
−
e
((
n
−
1
)
T
)]]
.
(5)
Feedback control enables the piezoelectric actuator to reduce
error,
e
(
t
)
, in position and, therefore, its velocity. The PID para-
meters not only influence the response speed of the controller
but also introduce energy into the system resonant modes, which
degrade its performance. A low-pass filter was placed in line
FIG. 4.
Schematic of the basic digital control loop.
with the feedback controller to limit the impact of the resonant
frequency modes of the actuator.
20
Figure 4 shows a schematic
block diagram illustrating the digital PID controller and the
filter.
C. Laser Doppler vibrometer
Single-point laser Doppler vibrometer (LDV) measurements
were performed with a Polytec OFV-3001 vibrometer to monitor
the velocity profile of the piezoelectric Doppler velocity drive. LDV
is a non-contact technique for probing vibrations of a surface. Dur-
ing an LDV measurement, a beam from a laser
(
f
0
)
is split into a
test beam and a reference beam. A Bragg cell adds a frequency shift
(
f
b
)
to the test beam that is directed to the target (piezoelectric actu-
ator). The motion of the target adds a Doppler shift frequency to
the beam given by
f
d
=
2
v
(
t
)/
λ
, where
λ
is the wavelength of the
beam and
v
(
t
)
is the velocity of the target. The resulting frequency
of the beam measured at the detector is a frequency modulated signal
f
mod
=
f
b
+
2
v
(
t
)/
λ
, from which the velocity vs time is obtained.
21,22
III. RESULTS
In open loop operation (without feedback control), Fig. 3 shows
a number of peak distortions and broadenings of the six peaks from
α
-iron. Also shown is a mechanical resonance in the error signal
e
(
t
)
near
−
6 mm/s. This originated with the stack of piezoelec-
tric elements becoming loose at the corresponding extension. This
problem was minimized by applying a DC offset to the drive sig-
nal to keep the piezoelectric stacks in a state of expansion. This DC
bias was used for closed loop, too. The feedback-controlled piezo-
electric Doppler velocity drive was optimized by tuning the PID
parameters and measuring the velocity profile
y
(
t
)
with the LDV.
A sinusoidal transition at the maxima and minima of the velocity
Rev. Sci. Instrum.
94
, 115107 (2023); doi: 10.1063/5.0157651
94
, 115107-3
Published under an exclusive license by AIP Publishing
14 November 2023 23:36:47