2. GALL et al.: INVESTIGATION OF PIEZOELECTRIC EFFECT AS MEANS TO GENERATE X-RAYS 107
Fig. 1. Bar-shaped piezoelectric material for increasing an applied voltage.
Fig. 2. Simulated voltage gain versus frequency of a lithium niobate bar. Gain
A mass of lithium niobate in the shape of a flat bar is shown is normalized to maximum gain value.
in Fig. 1. A detailed description of the material properties of
lithium niobate can be found in a number of sources [16]–[19].
The primary geometric axes of the bar in Fig. 1 are x1 , x2 , and
x3 , and the secondary axes x2 and x3 are rotated by an angle
θ about the primary axis x1 [20]. This rotation indicates the
crystallographic polarization direction of the lithium niobate.
Input electrodes, shown as gray regions on the top and bottom
(not visible) surfaces of the bar in Fig. 1, are used to deliver
electrical power to the crystal. Electric fields in the x3 -direction
couple into mechanical displacements in the x2 -direction as Fig. 3. Piezoelectric transformer equivalent circuit model.
a result of the rotated polarization, and an output voltage is
produced at the extremity of the bar. This is known as the length
extensional mode [21].
The voltage gain can be maximized by satisfying two criteria.
First, the product of the piezoelectric coupling coefficients
k23 and k33 should be maximized. The value of the product
k22 k32 has been found to be a maximum of approximately 0.3
when the polarization of lithium niobate is rotated by 45◦ [20].
Second, the piezoelectric bar should be driven at or near its
natural mechanical resonance. The resonant frequency ωn is Fig. 4. Experimental setup to generate X-rays using a piezoelectric crystal.
determined by material properties and the dimensions of the
bar, shown in the following [13]: III. E XPERIMENTAL S ETUP
The piezoelectric crystals used in this experiment were
nπ sE
ωn = . (4) 100 mm × 10 mm × 1.5 mm slabs of lithium niobate rotated
l ρ 45◦ about the x1 -axis, as shown in Fig. 1. Electrodes were
applied using silver paint with a measured layer thickness
The variables l, sE , and ρ are the length of the bar in the of approximately 50 μm. High field electron emitters were
x2 -direction, the elasticity tensor, and the density of the ma- fabricated from 0.1-mm-diameter platinum–iridium wire [23],
terial. The integer value n indicates the harmonic mode of cut to approximately 1 mm in length, and adhered to the high-
resonance. The plot in Fig. 2 was generated from solutions of voltage output of the crystal with silver paint. Fig. 4 shows the
a 1-D piezoelectric model based on the material constants for experimental setup for the piezoelectric X-ray source. All ex-
lithium niobate to demonstrate the voltage gain dependence on periments were conducted at pressures below 10−3 torr because
operating frequency [22]. this was the threshold pressure for X-ray production. Finite-
An equivalent circuit model for the piezoelectric transformer element simulations indicated that a maximum mechanical dis-
is shown in Fig. 3. A sinusoidal voltage source Vin drives placement of approximately 10 μm occurred at each extremity
the transformer input, which is modeled as a capacitor Cin of the bar with a displacement null located near its center [24].
representing the capacitance between the two input electrodes. For this reason, the crystal was clamped with an expanded
A step-up transformer models the voltage gain and the isolation polymer sponge at its center to reduce mechanical damping.
between the input and output terminals of the piezoelectric The high voltage at the crystal output was indirectly mea-
transformer. The output of the transformer is modeled as a sured using the bremsstrahlung spectra produced when the
capacitor Cout . The electron beam is modeled as a series of accelerated electron beam struck the stainless steel vacuum
diode and resistor with a parallel capacitor. The output and chamber walls. Electron trajectories were determined using
input of the transformer share a mutual ground. finite-element ray tracing software [24], shown in Fig. 4 as
3. 108 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 1, JANUARY 2013
TABLE I
P ERTINENT D ECAY P ROPERTIES OF C D -109 AS AN X-R AY
D ETECTOR C ALIBRATION S OURCE
Fig. 6. System diagram for the basic experimental configuration for piezo-
electric crystal operation. (A) Low-voltage ac drive signal at 25–50 mVmax
and 30.7 kHz. (T1 and T2) Falling edge trigger and gate signal for PX4. (B1,
B2, and B3) High-voltage ac drive signal at 10–20 Vmax to Pearson coil,
oscilloscope, and crystal. (D) Crystal-generated X-ray flux. (E) Raw analog
X-ray detector signal. (F) Digital spectrum data.
Fig. 5. Sample calibration spectrum using the CdTe X-ray detector for a
Cd-109 radioisotope calibration source.
dotted lines. Bremsstrahlung interactions occurred at the walls
of the port, and an Amptek XR-100T CdTe γ/X-ray detector
with 1.5-keV FWHM energy resolution and 4.0-μs resolving
time was used to record the X-ray spectra through a 50-μm-
thick aluminum window. A PX4 pulse processor was used to
digitize the spectrum for viewing on a PC. In this configuration,
the noise introduced by the PX4 signal gain was negligible Fig. 7. Input voltage and current traces for a resonating piezoelectric crystal.
because it was several orders of magnitude less than the noise
produced by the CdTe detector itself [25]. The detector was in Fig. 6 shows this setup. An example of a typical resonant
placed very near to this window to maximize the geometric burst pulse used to drive the crystal is shown in Fig. 7. The
efficiency of the detector and increase the signal–noise ratio. input voltage amplitude diminished throughout the pulse, while
The MCA was calibrated using a Spectrum Techniques the input current amplitude increased, an indication that the
1-μCi Cd-109 calibration source for the CdTe X-ray detector. resonant frequency had been reached [13]. The drive frequency
Cd-109 is a convenient choice because it has prominent peaks was in agreement with the modeled resonant frequency in
at 22 and 88 keV, providing an accurate calibration throughout Fig. 2, ranging between 30.6 and 30.9 kHz.
the range of the spectrum [26]. A peak at 24.9 keV was used as a A gate signal was applied to an Amptek PX4 digital pulse
third point to verify the calibration. A lower level discriminator processor in order to decrease the effect of background radi-
was fixed, and the MCA gain was set to 9.1 throughout the ation during sampling intervals. This was done because the
experiment, producing a range of detectable X-ray energy crystal is operated in a pulsed mode with a duty cycle of ap-
from 8 to 140 keV. Table I shows select decay properties of proximately 9% to limit mechanical failure of the crystal [13].
Cd-109. Fig. 5 shows a sample calibration spectrum of the The gate signal pulse is shown in Fig. 7 as an encapsulation of
Cd-109 source. the applied burst pulse and the immediately subsequent ring-
An Agilent 33210A function generator was used to produce down. This portion of the ring-down was arbitrarily defined
the ac voltage to drive the piezoelectric crystal. An Amplifier as the 5 ms after the pulse and was included to count X-rays
Research KAA1020 25-W 43-dB RF power amplifier was used measured during this time. A 90-μs zoomed view shows that the
to amplify the drive voltage to 11–16 Vmax . At drive voltages current and voltage waveforms are in phase with one another at
lower than this range, X-ray production was not observed, and resonance.
at higher voltages, the piezoelectric crystal tended to fracture
due to exceeding the yield strength of lithium niobate (between
IV. R ESULTS
30 and 120 MPa) [19]. A Pearson 2877 current monitor with
1-V/A output sensitivity measured the input current to the X-ray spectra were recorded which demonstrate that a piezo-
crystal. A Tektronix TDS 2024B oscilloscope was used to electric crystal designed to operate in the length extensional
measure crystal input voltage and current. The system diagram mode was capable of producing X-rays with energies up to
4. GALL et al.: INVESTIGATION OF PIEZOELECTRIC EFFECT AS MEANS TO GENERATE X-RAYS 109
Fig. 9. Same spectrum from Test 1 presented in total counts to demonstrate
time-dependent count rate reduction.
Fig. 8. Collection of nine high-energy X-ray tests under a variety of operating
conditions using a piezoelectric crystal. Spectra are presented in counts per output of the piezoelectric crystal and the effective resistance
second, and background was normalized and subtracted from each spectrum.
Duration for each test was between 30 and 60 s.
of the electron beam due to field emitter quality. Models have
shown that this 50-Ω variability in input impedance changes the
TABLE II input power by ±100 mW, in agreement with the experimen-
X-R AY S PECTRUM I NFORMATION FOR F IG .8. D URATION FOR A LL T ESTS tally observed range of input powers. The input voltage varied
I S B ETWEEN 30 AND 60 s. (∗ I NDICATES T EST W ITH
D EUTERIUM BACKGROUND G AS ) between 11 and 16 V in amplitude. Comparing this value with
the X-ray spectrum data in Fig. 8, the maximum measured gain
of the piezoelectric transformer source was between 7.9 and
11.5 kV/V.
An expression for the maximum electron beam current was
computed by applying energy conservation laws to the piezo-
electric transformer. The piezoelectric transformer model is
analogous to that of the conventional magnetic core transformer
such that the output current can be determined if the output
voltage and input power are known, as shown in
Pin = Vout × Iout . (5)
127 keV under several different conditions. A collection of
nine different X-ray spectra are shown in Fig. 8. Table II Using the data from Test 1, the input voltage and current
gives pertinent data for the spectra in Fig. 8 and shows that amplitudes were 16 V and 79 mA, respectively. Converting
high voltage was achieved with various pressures and crystal these values to rms and multiplying yield an input power of
samples. Test 9 shows that the piezoelectric crystal reached 632 mW. The peak output voltage was recorded to be 127 kV
127 keV in a deuterium environment at 770 μtorr, demonstrat- or 89.8 kV rms, and solving for Iout in (5) yields an rms current
ing that the method is viable in low-pressure gas applications. of 7 μA or a peak current of approximately 10 μA.
The spectra were binned to decrease counting error and improve An unexpected observation was made during this experiment
endpoint determination. Some energy resolution is sacrificed regarding the time-dependent X-ray output of the piezoelectric
due to the binning process. As a result, each energy level crystal. It was found that X-ray count rate and maximum
corresponds approximately to a ±7-keV range, and a precise X-ray energy both decreased as testing runtime progressed.
endpoint energy cannot be obtained. However, as the primary This limited data collection to approximately 1 min of active
goal of this work is to verify high-energy X-ray production, this collection time. The spectrum in Fig. 9 was generated from the
reduction of energy resolution is acceptable. spectral data from Test 1, showing the total counts collected
Of the nine spectra shown, five produced X-rays with an within two successive time periods, each lasting 60 s. The iron
endpoint energy of at least 127 keV. The variation in count kα peak of 6.4 keV was visible at both times, but there were two
rate among observations was due to uncontrolled factors such orders of magnitude of separation between the total counts in
as field emitter quality and variability in stray capacitances each of the time periods. The maximum X-ray energy recorded
at the output. Background counts were subtracted from each in the first 60 s reached the 127-keV bin according to Fig. 8,
recorded spectrum, and only statistically significant count rates but Fig. 9 shows that this decreased to about 15 keV in the
are shown. Error bars correspond to one standard deviation of next 60 s.
error and include the propagation of background counting error. One explanation for the decrease in X-ray count rate is
The function generator was fixed at a constant voltage; that electron beam transport discharged the output capacitance
however, input power varied between 312 and 720 mW among of the transformer. The circuit model in Fig. 3 shows that
observations. Modeling has indicated that variations in output a current return path was not available to the output of the
impedance can change the input impedance of the piezoelectric transformer, which prevented charge neutralization at the output
crystal by as much as 50 Ω. This variation in impedance is while the beam was off. Due to the low output capacitance
due to uncontrolled parameters such as stray capacitance at the of the transformer (calculated to be between 0.1 and 1 pF),
5. 110 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 1, JANUARY 2013
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[1] R. Talman, Accelerator X-Ray Sources. Hoboken, NJ: Wiley-VCH,
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Lab., Lemont, IL, Tech. Rep., Jul. 1996.
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[4] J. A. Geuther and Y. Danon, “High-energy x-ray production with pyro-
electric crystals,” J. Appl. Phys., vol. 97, no. 10, pp. 104 916-1–104 916-5, Brady Gall (S’09) received the B.S. and M.S. de-
May 2005. grees in electrical engineering from the University of
[5] W. Tornow, S. Lynam, and S. Shafroth, “Substantial increase in acceler- Missouri, Columbia, in 2009 and 2012, respectively.
ation potential of pyroelectric crystals,” J. Appl. Phys., vol. 107, no. 6, He is currently a Graduate Research Assistant with
pp. 063302-1–063302-4, Mar. 2010. the Department of Electrical and Computer Engi-
[6] J. Hird, “A triboelectric x-ray source,” Appl. Phys. Lett., vol. 98, no. 13, neering, University of Missouri, under the advise-
pp. 133 501-1–133 501-3, Mar. 2011. ment of Scott D. Kovaleski. His research focuses on
[7] A. Benwell, S. Kovaleski, and M. Kemp, “A resonantly driven piezoelec- the testing and optimization of high-voltage piezo-
tric transformer for high voltage generation,” in Proc. IEEE Int. Power electric sources for the production and acceleration
Modul. High Volt. Conf., May 2008, pp. 113–116. of charged particles.
6. GALL et al.: INVESTIGATION OF PIEZOELECTRIC EFFECT AS MEANS TO GENERATE X-RAYS 111
Scott D. Kovaleski (M’99–SM’09) received the B.S. Baek Hyun Kim (M’11) received the B.A. degree in physics from Chungnam
degree in nuclear engineering from Purdue Univer- National University, Daejeon, Korea, in 2001 and the M.S. and Ph.D. degrees
sity, West Lafayette, IN, and the M.S. and Ph.D. in materials science and engineering from the Gwangju Institute of Science and
degrees in nuclear engineering with a specialty in Technology, Gwangju, Korea, in 2003 and 2008, respectively.
plasma physics from the University of Michigan, In 2008, he joined the Department of Materials Science and Engineering,
Ann Arbor. Carnegie Mellon University, Pittsburgh, PA, as a Postdoctoral Research As-
From the University of Michigan, he moved on sociate. Since 2010, he has been a Postdoctoral Fellow with the Department
to General Electric (GE) Lighting, where he was of Electrical and Computer Engineering, University of Missouri, Columbia.
a Product Scientist working on quartz metal halide His research interests include low-dimensional nanostructures and optical and
arc lamps. From GE Lighting, he became a Con- electrical devices using low-dimensional nanostructures.
tractor with Glenn Research Center, NASA, where Dr. Kim is a member of the Materials Research Society, Korean Physical
he worked on the International Space Station plasma contactor and on ion Society, and Korean Vacuum Society.
propulsion. Since 2003, he has been with the University of Missouri, Columbia,
where he has worked on numerous research projects in the areas of compact
accelerators, plasma and ion sources, electric propulsion, and pulsed power. He Jae Wan Kwon (S’96–M’04) received the B.S. degree in electronics engineer-
and his students have conducted studies in pulsed-power engineering relevant ing from Kyungpook National University, Daegu, Korea, in 1994 and the M.S.
to flashover insulation of high-voltage accurate laser triggering of gas-filled and Ph.D. degrees in electrical engineering from the University of Southern
switches and solid-state pulsed-power switching. He has developed and studied California, Los Angeles, in 1997 and 2004, respectively.
compact ion accelerators and ion sources based on piezoelectric transformer He is currently an Associate Professor with the Department of Electrical and
high-voltage sources for space propulsion and compact neutron generators. His Computer Engineering, University of Missouri, Columbia, where he also holds
research interests include nuclear science, accelerators and plasmas, energetic a courtesy appointment with the Department of Biological Engineering. His
particle sources, and related technologies. research interests include micro-/nanoelectromechanical systems, micro power
Dr. Kovaleski is a member of the American Physical Society and the sources, microfabrication processing technology, piezoelectric transducers, mi-
American Nuclear Society. crofluidic systems, biomedical microsystems, and nanotechnology.
Prof. Kwon was a recipient of the NSF CAREER Award, Missouri Honor
Junior Faculty Research Award, Outstanding Paper Award in the IEEE In-
ternational Conference on Solid-State Sensors, Actuators and Microsystems
James A. VanGordon (S’07) received the B.S. and (Transducers 2009), and the Best New Application Paper Award from IEEE
M.S. degrees in electrical engineering from the Uni- T RANSACTIONS ON AUTOMATION S CIENCE AND E NGINEERING (2006). He
versity of Missouri, Columbia, in 2008 and 2010, has been serving on the Technical Program Committees of the International
respectively, where he is currently working toward Workshop on Micro and Nanotechnology (PowerMEMS), the IEEE Conference
the Ph.D. degree in electrical engineering. on Sensors, and the Hilton Head Solid-State Sensors, Actuators and Microsys-
His research interests include pulsed-power sys- tems Workshop.
tems, power electronics, and high-voltage circuit
design.
Mr. VanGordon is a student member of the Insti- Gregory E. Dale (S’97–M’03) received the B.S. degree in nuclear engineering
tute of Nuclear Materials Management. from The University of New Mexico, Albuquerque, in 1995, the M.S. degree
in nuclear engineering with a minor in physics from North Carolina State
University, Raleigh, in 1998, and the Ph.D. degree in electrical engineering
from the University of Missouri, Columbia, in 2003.
Upon completing his dissertation, he joined Los Alamos National Laboratory
Peter Norgard (S’02–M’09) received the M.S. and Ph.D. degrees in electrical
(LANL), Los Alamos, NM, as a Technical Staff Member developing solid-
engineering from the University of Missouri, Columbia, in 2006 and 2009,
state pulsed-power modulators for compact accelerator systems. He is currently
respectively.
a Project Leader with the High Power Electrodynamics Group, Accelerator
He is currently a Postdoctoral Research Fellow with the University of
and Operations Technology Division, LANL. In this capacity, he is in charge
Missouri, where he is conducting research on ion sources and accelerators and
of several compact radiography, pulsed-power, compact neutron source, and
on electrooptic voltage and current diagnostic techniques.
accelerator production medical radioisotope projects. He has experience in
experimental research, solid-state modulators, electron accelerators, nuclear
medicine, radiography, electrothermal plasma guns, first-wall components in
tokamak fusion reactors, radiation shielding, and radiation detection.
Andrew Benwell (M’09), photograph and biography not available at the time Dr. Dale serves on the Executive Committee of the International Power
of publication. Modulator and High Voltage Conference.