Impedance Spectroscopy Characterization of Highly Attenuating Piezocomposites

Transcription

1 CN 6 - Poter 9 Ieance ectrocoy Characterization of Highly Attenuating Piezocooite Anrey RYBIAN, Yora HL, Ultrahae Lt., el-aviv, Irael Ron AKR, AI echnical oftware Inc., Kington, Ontario, Canaa Abtract. hi aer reent the reult of a coarative exeriental invetigation of rorietary olyer-free olycrytalline cooite (orou ceraic, iezocooite ceraic/crytal) eveloe an anufacture by Ultrahae Lt. Both the I tanar an ultraonic etho together with the Piezoelectric Reonance Analyi Progra (PRAP) were ue to eterine aterial contant. he PRAP oftware (AI echnical oftware Inc.) enable colete autoatic analyi of reonance ieance ectra by coaring the reicte eenence of ieance on frequency with an ieance ectru eaure on a ale of aroriate geoetry an ienion to erive colex elatic, ielectric, an iezoelectric roertie of the reonator. Material contant obtaine by the ifferent etho were coare. he reult how that the ieance ectrocoy etho give ore recie ata an in oe cae i the heet anchor of correct value for aterial with extreely low Q.. Introuction ean on eical an N ultraonic tranucer erforance have increae in recent year. Low-Q iezoceraic an iezocooite aterial are wiely ue for wie-ban N ultraonic tranucer with high enitivity an reolution. oe of thee avance aterial are loy an irect ue of I tanar for aterial contant eterination lea to ignificant error. he oeling an eign of iezoelectric evice by finite eleent etho, aong other, relie on the accuracy of the ielectric, iezoelectric an elatic coefficient of the active aterial ue; coonly an aniotroic ferroelectric olycrytal. he accurate ecrition of iezoceraic ut inclue the evaluation of the ielectric, iezoelectric an echanical loe, accounting for the out-of-hae aterial reone to the inut ignal. he baic technique for fining aterial contant of iezoelectric aterial are outline in the I tanar on Piezoelectricity (987) []. hee etho work for any of the ot wiely ue coercial iezoceraic bae on lea-titanate-zirconate (PZ) cooition that are high-q M an high-couling coefficient iezoelectric aterial. However, there i a general agreeent that their ue in any new iezoelectric aterial uch a orou ceraic, iezoelectric olyer or iezoelectric cooite ay lea to ignificant error. Furtherore, the current I tanar oe not corehenively account for the colex nature of aterial coefficient, uing only the ielectric lo factor (tan δ) an the echanical quality factor (Q M ) to account for lo. Nuerou technique uing colex aterial contant have been rooe to take into account loe in low-q M aterial an to overcoe liitation in the I tanar [-6]. Iterative etho [7-9] rovie the way to accurately eterine the colex

2 coefficient in the linear range of ole iezoceraic fro colex ieance reonance eaureent. he PRAP autoatic iterative etho [] ha been alie in thi work to the full et of tanar geoetrie an reonance oe neee to colete colex characterization in a wie range of aterial with very high an oerate lo factor.. Piezoelectric Reonance Analyi Metho In the irect iezoelectric effect charge i generate fro alying a tre to a ecien. In the convere iezoelectric effect, the ecien will unergo train in reone to an electric fiel. By conieration of four oible theroynaic otential in the cae of aiabatic, iotheral an low alitue conition [,], the linear equation of iezoelectricity give the relationhi between electric fiel (), ielectric ilaceent (), train () an tre (): n n q q g g + β () n n q q + + () n n q q e e c + () n n q q h h c β (4) In equation (-4), e, g, an h are the iezoelectric contant, an c are the elatic coliance an tiffne at contant an, an an β are the erittivity an invere erittivity at contant an. he echanical variable have three aitional hear irection (4, 5, 6) while the electrical variable are only in the three tanar irection (,, ). ach of the above et of equation i tyically rereente a the iezoelectric atrix with the tranoe of the iezoelectric contant in the to right corner. yetry in aterial ean that any of the eleent of the iezoelectric atrix are either equal, zero, or oe function of theelve. Pole olycrytalline aterial are of the C or 6 yetry, an iilar to the other et of equation, equation et () reuce to a for of the iezoelectric atrix that inclue only ineenent contant: ( ) (5)

3 In general the aterial contant are teerature (relative to the Curie teerature for ferroelectric), tie (logarithic relaxation ince oling) an frequency eenant. In reality the roertie ay alo be fiel-eenant which woul require a re-erivation of the iezoelectric equation for higher orer fiel ter. Ieance ectrocoy characterization te fro the relation for ieance Z: Z V I x A, (6) t where V i voltage, I i current, an A i the urface area over which current i eaure. he iezoelectric equation give the relationhi between an through tre an train. For ile -ienional reonance oe, any of the electric an echanical fiel variable go to zero an the et of iezoelectric equation ecoule. olving the wave equation for one-ienional teay-tate ilaceent in the ecien an evaluating fro the erivative of ilaceent, together with the bounary conition of an unclae reonator, the iezoelectric equation can be ue to evaluate the relationhi between an a a function of frequency an aterial roertie. he ieance of a thickne extenional () reonator reuce to []: h ωl ρ l ρ ω β + tan c c Z, (7) iωa where ρ i ecien enity, ω i angular frequency an l i thickne of the ale in the irection of oling. For the reonator the lateral ienion ut be at leat tie the thickne to aure a clean -ienional oe. hi can be relaxe lightly in low Q aterial. In ieance ectrocoy characterization of iezoelectric the aterial roertie of equation (7) can be ajute until the ieance fit a eaure ieance ectru a a function of frequency. he coon one-ienional 6 oe inclue the Length xtenional (L), hickne xtenional (), Length-hickne xtenional (L), hickne hear (), Length hear (L), an Raial oe. ach of thee oe rovie electrical, elatic an iezoelectric roertie of the aterial. able lit the roertie of one for of the reuce iezoelectric atrix with the oe that will rovie thoe roertie. able. Proertie Provie by the Coon Moe Proerty 55 5 Moe, L L, L, Raial L L, L, L, L L, Raial Raial Raial By analyzing ecien inucing the, L an Raial oe, all but of the reuce 6 iezoelectric atrix can be obtaine. can be foun fro the roertie eterine with the, L an L oe for other rereentation of the iezoelectric linear equation [8] eaning all oe but the L oe are require to contruct the iezoelectric atrix. Alternatively, uing an initial gue for the reuce atrix can be inverte an c coare that foun for the oe, eliinating nee for the L oe. In ractice, aterial roertie are ierive (vary with frequency). hi ean that the range of frequency ue to fit for of equation (6) to eaure ectra houl be liite. It i worth noting that only a few oint in the ectru are require to eterine roertie. For the oe, only three oint are require. he I tanar on Piezoelectricty (987) [] ecribe two aroache to obtaining aterial roertie uing either the ifference between arallel (f ) an erie (f ) reonance frequencie, or the frequency ratio between ifferent orer reonance eak. hi

4 can be robleatic when aterial roertie are ierive or when a low electroechanical couling contant reult in a all ifference between f an f. it [8] rooe a general etho for the,, L an L reonator uing three oint aroun reonance. hi etho oe not rely on critical frequencie in the ectru an o oe not loe enitivity for low Q aterial. At reonance an anti-reonance, current can be very large an all an thi reent an intruentation roble. hough le an iue for low Q aterial, it etho i le eaning of intruentation than the I etho. Finally, becaue the choice of analyi oint i oewhat arbitrary, noiy ectra an ale with oe couling ay till be analyze uing it etho. he I tanar in Piezoelectricity (987) treat all aterial roertie a real, evaluating echanical an electrical lo ineenently through Q M an tanδ. Loe in the electroechanical couling contant were aue zero. hi wa accetable for low lo iezoelectric aterial uch a PZ, but can lea to ignificant error when aterial have large lo. In real aterial the colex ieance reult fro colex aterial roertie []. hi i irectly aociate with ielectric conuction loe [4] an attenuation of the ilaceent wave in the ale. he Piezoelectric Reonance Analyi Progra [] analye ieance ectra to eterine colex aterial roertie. hi oftware ue a generalize for of it etho to eterine aterial roertie for any coon reonance oe, an a generalize ratio etho for the raial oe [5] vali for all aterial Q. By analyzing on each haronic, colex aterial roertie a a function of frequency can be eterine. he oftware alway generate an ieance ectru fro the eterine roertie to inicate valiity of the reult.. xeriental Reult an icuion he extreely low-q iezoceraic cooite A85L- an oerately low-q orou ceraic U- anufacture by Ultrahae Lt. were choen for coarion between the I tanar an PRAP etho of reonance eaureent. Colex electrical coefficient of iezocooite eleent were eterine by ieance ectrocoy etho uing Piezoelectric Reonance Analyi (PRAP) oftware []. Meaureent were ae uing the olartron Ieance/Gain-Phae Analyzer L 6. oun velocity an attenuation of longituinal wave in cooite ale were eaure by ule echo an through-tranit ultraonic etho in the frequency range -5 MHz uing a LeCroy Wave urfer 4 igital ocillocoe an Olyu 58 an 577 uler/receiver uing tanar Olyu tranucer. Figure an how ieance ectra an PRAP aroxiation for thickne an raial oe of A85L- iezoceraic cooite ik (Øx.8 ). Colex contant of A85L- ik (Ø x.8 ), obtaine uing PRAP analyi for thickne an raial reonance oe a well a correoning I tanar reult are uere in able an. Aitional hyical araeter of A85L- cooite eaure by ultraonic etho are a follow: Z A.8 MRayl, ρ 6.4 g/c, V t 568 /c., Q M. 4

5 Figure. Ieance ectra an PRAP aroxiation for oe of A85L- ik. Figure. Ieance ectra an PRAP aroxiation for raial extenional oe of A85L- ik. It can be een fro able an that the icreancy between PRAP an I tanar reult for very low-q ceraic cooite were greater than 5%. he new ceraic iezocooite A85L- anufacture by Ultrahae Lt. i characterize by reviouly unachievable low Q (Q t M) cobine with high iezoelectric () an electroechanical (k t.5) araeter, high Curie oint (4 C) an low acoutic ieance ( MRayl) in a wie working frequency range (.- MHz). For lower k ale even greater ifference woul be execte. PRAP Paraeter able. PRAP Analyi Reult for Moe of A85L- ik Real Iaginary I tanar %rror f (Hz) f (Hz) k t c (N/²) c (N/²) e (C/²) h (V/) (F/)

6 able. PRAP Analyi Reult for Raial xtenional Moe A85L- ik PRAP Paraeter Real Iaginary I tanar %rror f (Hz) f (Hz) f (Hz) (²/N) (²/N) (C/N) (F/) k σ P e (C/²) (²/N) C 66 (N/²) Figure how ieance ectra an PRAP aroxiation for the oe of a U- orou ceraic ik (Øx.5 ). Colex contant for a U- ik (Ø x.5 ) with oerately low Q obtaine uing PRAP analyi for thickne an raial reonance oe a well a correoning I tanar reult are uere in able an 4. Aitional hyical araeter of U- orou ceraic eaure by the ultraonic etho for a ic are a follow: Z A 5.5 Mrayl, ρ 6.6 g/c, V t 875 /c., Q M 5. It i reaily oberve in able an 4 that for oerately low-q ceraic cooite the reult obtaine by PRAP an the I tanar etho are iilar. However, even in thi cae PRAP give et of colex contant, allowing thereby account an analyi of the loe. Porou ceraic U- anufacture by Ultrahae Lt. i characterize by the oerate low Q t M, high electroechanical couling factor k t.57, low acoutic ieance (5 MRayl) an are ue for eical an N ultraonic tranucer eign. Figure. Ieance ectra an PRAP aroxiation for oe of U- ik. PRAP wa ue to eterine aterial roertie fro higher orer haronic, an the reult are illutrate in Figure 4 an 5. Figure 4 how the ieance ectru an PRAP aroxiation for the econ orer eak ( natural haronic) of the oe of a U- orou ceraic ik. 6

7 able. PRAP Analyi Reult for Moe of U- ik PRAP Paraeter Real Iaginary I tanar %rror f (Hz) f (Hz) k t c (N/²) c (N/²) e (C/²) h (V/) (F/) able 4. PRAP Analyi Reult for Raial xtenional Moe U- ik PRAP Paraeter Real Iaginary I tanar %rror f (Hz) f (Hz) f (Hz) (²/N) (²/N) (C/N) (F/) k σ P e (C/²) (²/N) c 66 (N/²) Figure 4. Ieance ectra an PRAP aroxiation for econ orer eak ( natural haronic) of oe of U- orou ceraic ik Figure 5 how reult fro PRAP for colex c obtaine fro the haronic of the oe of a U- orou ceraic ik. It i reaily oberve that c (real) ecreae an c (iaginary) increae ignificantly with the frequency. herefore echanical quality factor Q M ecreae ignificantly a a reult of Rayleigh cattering of high frequency ultraonic 7

8 wave on ore. hi alo inicate the iortance of tating frequency with tabulate aterial roertie. Figure 5. Frequency eenence of c (real) an c (iaginary) obtaine by PRAP for higher orer eak of oe of a U- orou ceraic ik. 4. uary A coarative exeriental invetigation of rorietary olycrytalline cooite with very low an oerate Q M eveloe an anufacture by Ultrahae Lt wa reente. he I tanar on iezoelectricity an ultraonic etho together with the Piezoelectric Reonance Analyi Progra (PRAP) were ue to eterine aterial contant. Material contant obtaine by the ifferent etho were coare. he reult how that the ieance ectrocoy etho give ore recie ata an in oe cae i the heet anchor of correct value for aterial with extreely low Q. 8

9 Reference I tanar on iezoelectricity. ANI/I t M. Alguero, C. Aleany, L. Paro an A. M. Gonzalez. Metho for Obtaining the Full et of Linear lectric, Mechanical an lectroechanical coefficient an All Relate Loe of a Piezoelectric Ceraic. J. A. Cera. oc. 87 (), 9 (4). R. Hollan. Rereentation of ielectric, elatic an iezoelectric loe by colex coefficient. I ran.onic Ultraon. U-4 (), 8 (967).. herrit, H.. Wieerick an B.K. Mukherjee. Non-iterative valuation of the Real an Iaginary Material Contant of Piezoelectric Reonator. Ferroelectric 4, (99).. herrit, H.. Wieerick an B.K. Mukherjee. A colete characterization of the iezoelectric, ielectric an elatic roertie of Motorola PZH incluing loe an ierion. Meical Iaqinq 997: Ultraonic ranucer ngineerinq. PI Proceeinq. 7, 58 (997).. herrit, H.. Wieerick an B.K. Mukherjee. he Colete Matrix of the Piezoelectric, ielectric an latic Material Contant of - Piezoelectric Ceraic/Polyer Cooite, art Material. tructure, an Integrate vte, PI Proceeing, 4, 7 (997). C. Aleany, L. Paro, B. Jienez, F. Carona, J. Meniola an A.M. Gonzalez. Autoatic iterative evaluation of colex aterial contant in iezoelectric ceraic. J. Phv. : Al. Phy. 7, 48 (994). J.G. it. Iterative etho for accurate eterination of the real an iaginary art of the aterial coefficient of iezoelectric ceraic. I ran. onic Ultraon. U- (6), 9-4 (976). L.Paro, C. Aleany, J. Ricote, A. Moure, R. Poyato an M. Alguero. Iterative etho for the characterization of iezoelectric aterial with loe. Proc. Intern. Conf. Material technology an eign of integrate iezoelectric evice. Couurayeur, Italy, 45, 4. PRAP (Piezoelectric Reonance Analyi Progra). AI echnical oftware Inc. ( A.F. evonhire, Philohical Magazine uleent,, 85-, 954 W.P. Maon, Phyical Acoutic an the Proertie of oli (. Van Notran Co. Inc. Princeton 958)..A. Berlincourt,.R. Curran, H. Faffe, Phyical Acoutic I, Part A (W.P. Maon e., Acaeic Pre 964). L.C. hen, J.A. Kong, Alie lectroagneti (PW ngineering, Boton 98). C. Aleany, A.M. Gonzalez, L. Paro, B. Jienez, F. Carona an J. Meniola. Autoatic eterination of colex contant of iezoelectric loy aterial in the raial oe. J. Phv. : Al.Phv. 8(5), 945 (995). 9