GALL et al.: INVESTIGATION OF PIEZOELECTRIC EFFECT AS MEANS TO GENERATE X-RAYS 107Fig. 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 oflithium niobate can be found in a number of sources –.The primary geometric axes of the bar in Fig. 1 are x1 , x2 , andx3 , and the secondary axes x2 and x3 are rotated by an angleθ about the primary axis x1 . This rotation indicates thecrystallographic 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 deliverelectrical power to the crystal. Electric ﬁelds in the x3 -directioncouple 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 isproduced at the extremity of the bar. This is known as the lengthextensional mode . The voltage gain can be maximized by satisfying two criteria.First, the product of the piezoelectric coupling coefﬁcientsk23 and k33 should be maximized. The value of the productk22 k32 has been found to be a maximum of approximately 0.3when the polarization of lithium niobate is rotated by 45◦ .Second, the piezoelectric bar should be driven at or near itsnatural 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 thebar, shown in the following : 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 thicknessThe variables l, sE , and ρ are the length of the bar in the of approximately 50 μm. High ﬁeld electron emitters werex2 -direction, the elasticity tensor, and the density of the ma- fabricated from 0.1-mm-diameter platinum–iridium wire ,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 thea 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 becauseoperating frequency . 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 extremitythe transformer input, which is modeled as a capacitor Cin of the bar with a displacement null located near its center .representing the capacitance between the two input electrodes. For this reason, the crystal was clamped with an expandedA 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 thecapacitor Cout . The electron beam is modeled as a series of accelerated electron beam struck the stainless steel vacuumdiode and resistor with a parallel capacitor. The output and chamber walls. Electron trajectories were determined usinginput of the transformer share a mutual ground. ﬁnite-element ray tracing software , shown in Fig. 4 as
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 aCd-109 radioisotope calibration source.dotted lines. Bremsstrahlung interactions occurred at the wallsof the port, and an Amptek XR-100T CdTe γ/X-ray detectorwith 1.5-keV FWHM energy resolution and 4.0-μs resolvingtime was used to record the X-ray spectra through a 50-μm-thick aluminum window. A PX4 pulse processor was used todigitize 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 noiseproduced by the CdTe detector itself . The detector was in Fig. 6 shows this setup. An example of a typical resonantplaced very near to this window to maximize the geometric burst pulse used to drive the crystal is shown in Fig. 7. Theefﬁciency 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 the1-μCi Cd-109 calibration source for the CdTe X-ray detector. resonant frequency had been reached . The drive frequencyCd-109 is a convenient choice because it has prominent peaks was in agreement with the modeled resonant frequency inat 22 and 88 keV, providing an accurate calibration throughout Fig. 2, ranging between 30.6 and 30.9 kHz.the range of the spectrum . A peak at 24.9 keV was used as a A gate signal was applied to an Amptek PX4 digital pulsethird 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 theexperiment, 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 .Cd-109. Fig. 5 shows a sample calibration spectrum of the The gate signal pulse is shown in Fig. 7 as an encapsulation ofCd-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 deﬁnedthe ac voltage to drive the piezoelectric crystal. An Ampliﬁer as the 5 ms after the pulse and was included to count X-raysResearch KAA1020 25-W 43-dB RF power ampliﬁer was used measured during this time. A 90-μs zoomed view shows that theto amplify the drive voltage to 11–16 Vmax . At drive voltages current and voltage waveforms are in phase with one another atlower than this range, X-ray production was not observed, and resonance.at higher voltages, the piezoelectric crystal tended to fracturedue to exceeding the yield strength of lithium niobate (between IV. R ESULTS30 and 120 MPa) . A Pearson 2877 current monitor with1-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 extensionalmeasure crystal input voltage and current. The system diagram mode was capable of producing X-rays with energies up to
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 operatingconditions using a piezoelectric crystal. Spectra are presented in counts per output of the piezoelectric crystal and the effective resistancesecond, 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 ofnine different X-ray spectra are shown in Fig. 8. Table II Using the data from Test 1, the input voltage and currentgives pertinent data for the spectra in Fig. 8 and shows that amplitudes were 16 V and 79 mA, respectively. Convertinghigh voltage was achieved with various pressures and crystal these values to rms and multiplying yield an input power ofsamples. Test 9 shows that the piezoelectric crystal reached 632 mW. The peak output voltage was recorded to be 127 kV127 keV in a deuterium environment at 770 μtorr, demonstrat- or 89.8 kV rms, and solving for Iout in (5) yields an rms currenting 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 experimentendpoint determination. Some energy resolution is sacriﬁced regarding the time-dependent X-ray output of the piezoelectricdue to the binning process. As a result, each energy level crystal. It was found that X-ray count rate and maximumcorresponds 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 activegoal of this work is to verify high-energy X-ray production, this collection time. The spectrum in Fig. 9 was generated from thereduction 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 ironendpoint energy of at least 127 keV. The variation in count kα peak of 6.4 keV was visible at both times, but there were tworate among observations was due to uncontrolled factors such orders of magnitude of separation between the total counts inas ﬁeld emitter quality and variability in stray capacitances each of the time periods. The maximum X-ray energy recordedat 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 theare 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 capacitancehowever, input power varied between 312 and 720 mW among of the transformer. The circuit model in Fig. 3 shows thatobservations. Modeling has indicated that variations in output a current return path was not available to the output of theimpedance can change the input impedance of the piezoelectric transformer, which prevented charge neutralization at the outputcrystal by as much as 50 Ω. This variation in impedance is while the beam was off. Due to the low output capacitancedue to uncontrolled parameters such as stray capacitance at the of the transformer (calculated to be between 0.1 and 1 pF),
110 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 1, JANUARY 2013positive charge that accumulated at the output reduced the  J. Yang, “Piezoelectric transformer structural modeling—A review,” IEEEoutput voltage magnitude . This drop in voltage reduced the Trans. Ultrason., Ferroelect., Freq. Control, vol. 54, no. 6, pp. 1154–1170, Jun. 2007.electric ﬁeld necessary for electron ﬁeld emission, resulting in a  L. Hwang, J. Yoo, E. Jang, D. Oh, Y. Jeong, I. Ahn, and M. Cho, “Fab-drop in current as described by the Fowler–Nordheim equation. rication and characteristics of PDA LCD backlight driving circuits usingThe following shows the Fowler–Nordheim equation showing piezoelectric transformer,” Sens. Actuators A, Phys., vol. 15, no. 1, pp. 73– 78, Sep. 2004.that the electron beam current density J is dependent on electric  P. Bolhuis, “Gas discharge ﬂash lamp with piezoelectric trigger genera-ﬁeld E among other factors such as surface work function tor,” U.S. Patent 4 082 985, Apr. 4, 1978.φ, permittivity , and a dimensionless image force function  Y. Park, “Electrical properties of a piezoelectric transformer for an AC–DC converter,” J. Korean Phys. Soc., vol. 57, no. 4, pp. 1131–1133,f (y) : Oct. 2010.  H. Itoh, K. Teranishi, and S. Suzuki, “Discharge plasmas generated by E2 3 piezoelectric transformers and their applications,” Plasma Sources Sci. J = 1.54 × 10−6 −6.83×109 φ 2 f (y)/E . (6) Technol., vol. 15, no. 2, pp. S51–S61, May 2006. φ  A. L. Benwell, “A high voltage piezoelectric transformer for active inter- rogation,” Ph.D. dissertation, Univ. Missouri-Columbia, Columbia, MO,Assuming that all other variables are ﬁxed, a drop in voltage 2009.  S. D. Kovaleski, A. Benwell, E. Baxter, B. T. Hutsel, T. Wacharasindhu,at the transformer output due to discharging by the beam and J. W. Kwon, “Ultra-compact piezoelectric transformer charged par-leads to a decrease in beam current, thus reducing the X-ray ticle acceleration,” in Proc. Int. Workshop Micro Nanotechnol. Powerproduction rate of the system. The time-dependent decrease in Gener. Energy Convers. Appl., Washington, DC, Dec. 2009, pp. 399–402.  IEEE Standard on Piezoelectricity, ANSI/IEEE Std. 176-1987, 1988.counts could be mitigated by either increasing the capacitance  H. Jaffe and D. Berlincourt, “Piezoelectric transducer materials,” Proc.or incorporating a current return path at the transformer output. IEEE, vol. 53, no. 10, pp. 1372–1386, Oct. 1965.  R. S. Weis and T. K. Gaylord, “Lithium niobate: Summary of physical properties and crystal structure,” Appl. Phys. A, vol. 37, no. 4, pp. 191– 203, Aug. 1985. V. C ONCLUSION  Lithium Niobate/Lithium Tantalate, I. Crystal Technology.  K. K. Wong, Properties of Lithium Niobate. Maple Grove, MN: The data presented in this paper demonstrate how the piezo- Northstar Photonics, Inc, 2002.electric effect can be used to generate X-rays with energies  K. Nakamura and Y. Adachi, “Piezoelectric transformers using LiNbO3 single crystals,” Electron. Commun. Jpn. (Part III: Fundam. Electron.up to 127±7 keV. A lithium niobate piezoelectric crystal was Sci.), vol. 81, no. 7, pp. 1–6, Jul. 1998.designed to reach high voltages by electromechanically cou-  J. Yang and X. Zhang, “Extensional vibration of a nonuniform piezoce-pling a low-amplitude ac voltage to a high-amplitude output ramic rod and high voltage generation,” Int. J. Appl. Electromagn. Mech., vol. 16, no. 1, pp. 29–42, Jan. 2002.voltage. Electron ﬁeld emitters that were adhered to the surface  J. Yang, An Introduction to the Theory of Piezoelectricity, vol. 9, Advancesof the crystal directly extracted charge from the material. This in Mechanics and Mathematics. New York: Springer-Verlag, 2005.charge was then accelerated by the electric ﬁelds generated by  C. Bai, Scanning Tunneling Microscopy and Its Applications, 2nd ed. Shanghai, China: Scientiﬁc & Technical Publ., 1995.the crystal into a grounded metallic target. Interactions between  Comsol Multiphysics.the high-voltage electron beam and the metallic target produced  Personal Communication With Amptek Technical Staff, Aug. 2012.bremsstrahlung X-ray radiation. Discharging of the output ca-  Amptek, Inc, 14 Deangelo Drive Bedford, MA 01730 USA, How to Change the Full Scale Energy Range and Calibrate the Software.pacitance due to electron beam transport may have hindered  J. A. VanGordon, B. Gall, P. Norgard, S. Kovaleski, E. Baxter, B. Kim,X-ray production rates and maximum energy as runtime in- J. Kwon, and G. Dale, “Effects of capacitive versus resistive loading oncreased. As a result, X-ray production was limited to intervals high transformation ratio piezoelectric transformers for modular design considerations,” in Proc. IEEE Int. High Voltage Power Modul. Conf.,lasting approximately 60 s at a time. A complete characteri- Jun. 2012.zation of the piezoelectric X-ray source will be possible once  R. L. Ramey, Physical Electronics. Belmont, CA: Wadsworth Publ.the limitation to device runtime is resolved. To increase the Comp., 1961.duration of X-ray production, a current return path may needto be implemented which would prevent discharging at thetransformer output. R EFERENCES  R. Talman, Accelerator X-Ray Sources. Hoboken, NJ: Wiley-VCH, 2006.  H. Bizek, “The advanced photon source list of parameters,” Argonne Nat. Lab., Lemont, IL, Tech. Rep., Jul. 1996.  F. Pfeiffer, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Let., vol. 98, no. 10, pp. 108 105-1–108 105-4, Mar. 2007.  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  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-  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  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.
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 Physicalhe 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 compactaccelerators, 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 Southernswitches 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 andhigh-voltage sources for space propulsion and compact neutron generators. His Computer Engineering, University of Missouri, Columbia, where he also holdsresearch interests include nuclear science, accelerators and plasmas, energetic a courtesy appointment with the Department of Biological Engineering. Hisparticle 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 LaboratoryPeter 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 currentlyrespectively. 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 chargeMissouri, where he is conducting research on ion sources and accelerators and of several compact radiography, pulsed-power, compact neutron source, andon 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 Powerof publication. Modulator and High Voltage Conference.