1 U.P.B. Sci. Bull., Series A, Vol. 72, Iss. 2, 2010 ISSN PIEZOCERAMICS UNDER ELECTRON IRRADIATION Irinela CHILIBON 1 Lucrarea prezintă aspecte privind comportarea piezoceramicelor PZT la iradiere cu electroni de putere scazuta. Probele PZT au ost iradiate într-un accelerator liniar de electroni cu doze dierite de electroni, şi anume: 10 kgy; 15 kgy; 20 kgy; 25 kgy. Aceste ceramice îşi schimbă puţin perormanţele după iradierea cu electroni de putere scazută, însă la 25 kgy constantele piezoelectrice de sarcină şi de tensiune cresc mai mult. Totuşi, descompunerea parţială a PZT ar putea să apară la iradierea cu electroni de putere ridicată şi în consecinţă creşterea coeicienţilor de pierdere. O remarcă, probele experimentale iradiate prezintă proprietăţi dielectrice şi piezoelectrice cu variaţii mici, iar coeicienţii de cuplaj descresc chiar la doze mici de iradiere (sub 25 kgy). Rezultatele obtinute constituie punctul de plecare pentru proiectarea de materiale ceramice superioare cu parametrii îmbunătăţiţi, optime pentru aplicaţiile diverse ale traductoarelor piezoelectrice. Paper presents aspects concerning the behaviour o PZT piezoceramics at low power electron irradiation. The PZT samples were irradiated into a linear accelerator o electrons with dierent electron doses, namely: 10 kgy; 15 kgy; 20 kgy; 25 kgy. These ceramics change slightly their perormances ater low power electron irradiation, but at 25kGy the piezoelectric charge and voltage constants increase more. However, PZT partial decomposition could occur at high power electron irradiation doses and consequently the loosing coeicients enhance. As remark, the experimental irradiated PZT samples present piezoelectric and dielectric properties with small variations, and the coupling coeicients decrease even at small irradiation doses (below 25 kgy). The obtained results could be an excellent starting point in designing superior ceramic materials with improved parameters, suitable or various piezoelectric transducers applications. Keywords: piezoceramic, PZT, electron irradiation, electron accelerator 1. Introduction Piezoceramics represent a well-proven technology or abrication o electromechanical transducers. However, despite their widespread applications there are still many aspects o their behaviour that poorly understood this is particular true o nonlinear eects that characterize their dielectric, elastic, and piezoelectric properties . The piezoceramics are crystallite conglomerate erroelectrics materials with random orienting and the piezoceramic materials 1 Researcher, National Institute o R&D or Optoelectronics, INOE-2000, Bucharest-Magurele, ROMANIA,
2 186 Irinela Chilibon Pb(Zr x Ti 1-x )O 3 are solid solutions, obtained in the classical technology , utilizing oxide powders and impurities as base materials. The properties o piezoceramics are unction o the preparation process  and the luctuations may be caused by inhomogeneous chemical composition, mechanical dierences in the orming process, varying shrinkage and chemical modiication during iring, and by varying response to the poling treatment. A high degree o process control is essential in the manuacture o piezoceramics in order to insure a consistent product with respect to electrical and mechanical properties . PZT ceramics are piezoelectric material with the perovskit structure. The internal stress o PZT is induced by the para- to erro-electric phase transition at the Curie point during cooling process ater iring and the additional anisotropic internal stress is induced in perpendicular direction. Their physical, chemical, and piezoelectric characteristics can be tailored to speciic applications. These materials are used as electromechanical transducers in various applications. The purpose o this study is to investigate the dependence o dielectric, piezoelectric and mechanical properties o hard PZT ceramic at electron irradiation dose variation, produced by an electron linear accelerator. 2. Piezoelectric coeicients and relations Piezoelectric ceramics produce an electrical charge when a load is applied and deormation occurs. Piezoelectric ceramics can also produce orce or deormation when an electrical charge is applied. A piezoceramic is thereore capable o acting as either a sensing or transmitting element, or both. Since piezoceramic elements are capable o generating very high voltages, they are compatible with today's generation o solid-state devices - rugged, compact, reliable, and eicient. Relationships between applied orces and the resultant responses depend upon: the piezoelectric properties o the ceramic; the size and shape o the piece; and the direction o the electrical and mechanical excitation. To identiy directions in a piezoceramic element, three axes are used (Figure 1). These axes, termed 1, 2, and 3, are analogous to X, Y, and Z o the classical three dimensional orthogonal set o axes. The polar, or 3 axis, is taken parallel to the direction o polarization within the ceramic. This direction is established during manuacturing by a high DC voltage that is applied between a pair o electroded aces to activate the material. In shear operations, these poling electrodes are later removed and replaced by electrodes deposited on a second pair o aces. In this event, the 3 axis is not altered, but is then parallel to the electroded aces ound on the inished element. When the mechanical stress or strain is shear, the subscript 5 is used in the second place. Piezoelectric coeicients with double subscripts link electrical and mechanical quantities. The irst subscript gives the direction o the electrical ield
3 Piezoceramics under electron irradiation 187 associated with the voltage applied, or the charge produced. The second subscript gives the direction o the mechanical stress or strain. Several piezoceramic material constants may be written with a "superscript" which speciies either a mechanical or electrical boundary condition. The superscripts are T, E, D, and S, signiying: T = constant stress = mechanically ree; E = constant ield = short circuit; D = constant electrical displacement = open circuit; S = constant strain = mechanically clamped. As an example, K T 3 expresses the relative dielectric constant (K), measured in the polar direction ( 3 ) with no mechanical clamping applied. The electrical behaviour o an unstressed medium under the inluence o an electric ield is deined by two quantities - the ield strength E and the dielectric displacement D. Their relationship is: D = εe (1) in which ε is the material permittivity. The mechanical behaviour o the same medium at zero electric ield strength is deined by two mechanical quantities - the stress applied T and the strain S. The relationship here is: S = st (2) in which s denotes the compliance o the medium. Piezoelectricity involves the interaction between the electrical and mechanical behaviour o the medium. To a good approximation this interaction can be described by linear relations between two electrical and mechanical variables: E S = s T + de (3) T D = dt + ε E The choice o the independent variables (T - mechanical, and E - electrical) is arbitrary. A given pair o piezoelectric equations corresponds to a particular choice o independent variables. In a similar way it is possible to arrive at the ollowing ormulae: D E = gt + ; S = s D + gd (4) T ε D D E = hs + ; T = c S hd (5) S ε S E D = ds + ε E ; T = c S ee (6) In these equations, S D, S E, ε T, ε S, d and g are the main practical constants. The superscripts to the symbols denote the quantity kept constant under boundary conditions. In reality, Eqs 3 to 6 are tensor equations with, in the general case, 3 electrical quantities (in the X, Y and Z directions) and 6 mechanical ones including shear about the three axes. So, o each piezoelectric parameter, up to 18 varieties can exist and are indicated by subscripts. For piezoelectric materials the direction o polarization is usually taken to be that o the Z-axis (direction 3) (see
4 188 Irinela Chilibon Fig. 1). Methods o measurement and piezoelectric properties o ceramic materials and components are described by  . Fig. 1 Designation o the axis and directions o deormation Fig. 2 Equivalent electrical circuit o PZT disc The equivalent electrical circuit o PZT disc is a resonant circuit (Fig. 2) and is characterized by two requencies: s and p. At the series resonance, branch L - C a is in resonance, the lower branch o the equivalent circuit diagram becomes low-resistive and the impedance shows a minimum Z min. At the parallel resonance, the branch L - (C b + C a ) is in resonance, the resonant circuit becomes high-resistive and the impedance has a maximum Z max. Modern impedance analyzers (e.g. HP 4192A) can be combined with a computer and programmed to ind s, p, Z min and Z max The eective coupling actor k e then ollows rom the ormula (Fig. 3): k e 2 2 p s = (7) 2 p Fig. 3 Impedance at the planar resonance (measured at a disc φ 5 x 1 mm)
5 Piezoceramics under electron irradiation 189 It is also possible to determine k e o more complicated devices like bimorphs or PZT discs or plates glued on some substrate. Depending on the construction dierent values o k e will be ound. The translation to the absolute quality level is oten very complicated or impossible. However k e is always a useul relative measure or the eectiveness o a device. k 2 Ca = (8) e C + b Ca By using equations: 1 1 s = (9) 2π LCa and 1 Ca + Cb p = (10) 2π L CaCb This ratio can be expressed as a unction o series- and parallel resonant requency, p s k = (11) 2 p So it is possible to derive the coupling actor rom these resonant requencies. As an approximation, when ke <<1 one may write: p 2 s Δ k e 2 = 2 (12) s s The piezoelectric voltage constant g is deined as the electric ield generated in a material per unit mechanical stress applied to it. Alternatively, it is the mechanical strain experienced by the material per unit electric displacement applied to it. The irst subscript reers to the direction o the electric ield generated in the material or to the applied electric displacement the second reers respectively to the direction o the applied stress or to the direction o the induced strain. The piezoelectric charge constants d is deined as the electric polarization generated in a material per unit mechanical stress applied to it. Alternatively, it is the mechanical strain experienced by the material per unit electric ield applied to it. The irst subscript reers to the direction o polarization generated in the material (at E = 0) or to the applied ield strength, the second reers respectively to the direction o the applied stress or to the direction o the induced strain. The g and d constants o a material are inter-related by their dielectric constant. Thus
6 190 Irinela Chilibon d g = or g kε 0 = d (13) kε 0 where K is the dielectric constant and ε o is the permittivity o space, 9 x Farads per meter. For a given level o d constant, the g is high i the dielectric constant is low and vice-versa. The compliance s o a material is deined as the strain produced per unit stress. It's the reciprocal o the modulus o elasticity. The irst subscript reers to the direction o strain, the second to direction o stress. For example, the compliance s o a material determined or the piezoceramic plate is: E 1 s11 = (14) 2 2 4ρ L r D E 11 s11 1 k31 s 2 ( ) = (15) where ρ is the piezoceramic density, r is the resonance requency, L is the thickness o disc. The relation between d 31, k 31 and s 11 is the ollowing: d k T s E ε33 11 = (16) Whereas the relative dielectric constant is strictly a material property, the capacitance is a quantity dependent on the type o material and its dimensions. The capacitance is calculated by multiplying the relative dielectric constant by the 12 permittivity o ree space ( ε 0 = arads / meter ) and A electrode surace area, then dividing by the t thickness separating the electrodes. Units are expressed in arads. kε 0A C = (17) t K 3 is related to the capacitance between the original poling electrodes. K 1 is related to the capacitance between the second pair o electrodes applied ater removal o the poling electrodes or the purposes o shear excitation. The mechanical losses can be determined rom the mechanical quality or damping actor, Q M (18). 2 a Q M = (18) π r Z rc( a r ) Where C is the low requency capacitance and Z r is the minimum impedance, r is the resonance requency and a is the antiresonance requency. Also, when Q M > 3, Q M can also be determined approximately rom the requency response curve and the bandwidth at 3 db ( 2 1 ) as ollows: Q = r M (19) 2 1
7 Piezoceramics under electron irradiation Experiments and results The piezoceramic materials under study are solid solutions o PZT (lead titanate zirconate) Pb(Zr x Ti 1-x )O 3 obtained by classic technology in laboratory, using as raw materials oxide. Material selection should be based on the conditions o a given application. PZT ceramic is the active element into various piezoceramic transducers. Thereore, it is important to understand the behaviour o this material at the variation o electron irradiation doses. PZT material parameters were measured or two modes: planar and thickness, or complete characterization, by using disc samples o hard PZT material (7600 Kg/m 3 density), with small size (15 mm diameter, and 1.06 mm thickness). The research was made on many PZT samples, in order to have an accurate evaluation. Ater each electron irradiation the main electric, piezoelectric and dielectric characteristics o the piezoceramic materials were measured, namely: coupling coeicients (K e, k), piezoelectric coeicients (g 31, d 31 ), strain coeicients, and mechanical quality actor (Q m ). Reerring to the equivalent circuit o PZT disc, the dependence o ( s and p ) serial and parallel resonant requencies (in the planar and thickness modes), R impedance at resonant requency (in the planar and thickness modes) and the capacities (C a and C b ) upon irradiation doses are determined. The PZT disc samples were irradiated by an electron accelerator with dierent doses (between 10 and 25 kgy), and then the main electric, piezoelectric and dielectric characteristics o the PZT disc were measured. Electron accelerator has the ollowing parameters: energy 7 MeV, average beam current 7 ma, pulse width 2.5 ms, pulse repetition rate 150 Hz, electron irradiation dose 4 W10 3 Gy/min at 1 m. The PZT samples were irradiated by dierent electron doses, namely: 10 kgy; 15 kgy; 20 kgy; 25 kgy. According to , , the main parameters and characteristics o PZT piezoceramic were determined by HP 4194 Impedance/Gain-Phase Analyzer, Hewlett Packard, USA. The main measured or calculated parameters o the experimental PZT materials were: coupling coeicients, piezoelectric voltage coeicients, ree dielectric constant, mechanical quality actor in thickness mode and the elements o the equivalent electrical circuit (resonant requencies, resistance, and capacities). For better understanding o results, the main material parameters and characteristics as unction o electron irradiation doses are illustrated in the Figures 4 to 14. For the planar mode o PZT disc, the curves requency as unction o electron irradiation doses show small variations o parallel and serial requencies ( p and s ), (Fig. 4). However, in the thickness mode o PZT disc p decreases, and s increases (Fig. 5).
8 192 Irinela Chilibon Fig. 4 Frequency as unction o Dose in the Planar Mode or PZT disc Fig. 5 Frequency as unction o Dose in Thickness Mode or PZT disc For the planar and thickness modes o PZT disc, the curves R resistance as unction o electron irradiation doses increase (Fig. 6). Fig. 6 Resistance as unction o Dose or PZT disc
9 Piezoceramics under electron irradiation 193 Reerring to the equivalent circuit o the PZT disc (Fig. 2), the curves o C a and C b capacities unction o electron irradiation doses increase or the planar and thickness modes, with small variations (Fig. 7 and 8). Fig. 7 Capacity as unction o Dose in Planar Mode or PZT disc Fig. 8 Capacity as unction o Dose in Thickness Mode or PZT disc For the planar and thickness modes o the PZT disc, the mechanical quality actors Q m as unction o electron irradiation doses present small variations (Fig. 9). Fig. 9 Mechanical Quality Factor as unction o Dose or PZT disc
10 194 Irinela Chilibon For the planar and thickness modes, the eective coupling coeicients as unction o electron irradiation doses decrease that means the electromechanical eiciencies are smaller (Fig. 10 and 11). Fig. 10 Eective Coupling Coeicient as unction o Dose or PZT disc Fig. 11 Coupling Coeicients as unction o Dose or PZT disc The piezoelectric charge constant d 31 as unction o electron irradiation doses increases by 3% (Fig. 12). Fig. 12 Piezoelectric Charge Constant as unction o Dose or PZT disc
11 Piezoceramics under electron irradiation 195 The piezoelectric voltage constant g 31 as unction o electron irradiation doses increases by 14% (Fig. 13). Fig. 13 Piezoelectric Voltage Constants as unction o Dose or PZT disc The elastic constants (compliances) s 11e, s 11d, s 12e, and s 12e as unction o electron irradiation doses present small variations (Fig. 14). Fig. 14 Elastic Constants as unction o Dose or PZT disc As important result the values o piezoelectric coeicients increase in the range o 10 to 25 kgy electron irradiation doses. However, the values o coupling coeicients decrease. At 25 kgy electron irradiation doses, the piezoelectric charge constant d 31 increases by 3%, and the piezoelectric voltage constant g 31 increases by 14%. The other parameters present an acceptable stability with the irradiation doses.
12 196 Irinela Chilibon 4. Conclusions As experimental results, the irradiated PZT samples change their piezoelectric and dielectric properties, especially piezoelectric and voltage charge constants. These PZT materials are stable in time and can be successully utilized into piezoceramic transducers and devices which work in radiation environment, such as: nuclear reactors and centrals, etc. The coupling coeicients decrease at 25 kgy irradiation doses, and the piezoelectric charge and voltage constants increase. Usual, high g constants are wanted. However, the connections to the element, such as cables, act as suplimentary capacities, increase the losses and decrease the output voltage. Thereore, high dielectric and piezoelectric constants are also desirables to minimize the eects o the capacitive loads. In consequence, the study o piezoceramics at electron irradiation could promote research or superior ceramic materials with improved characteristics, suitable or various piezoelectric transducer applications . R E F E R E N C E S  D. A. Hall, Piezoelectric Materials: Advances in Science, Technology and Applications, NATO Science Series, Kluwer Academic Publisher, 76, 2000  K. Okazaki, Ferroelectrics, 41, 77-96, 1982  Z. Surowiak, D. Czekj, Inluence o the chemical composition on the physical properties o PZT-type piezoceramic, Molecular and Quantum Acoustics, , 2003  M. Brissaud, IEEE Transaction on Ultrasonics, 38, 6, 1991  IEEE Standards on Piezoelectricity. Special Issue o Trans. Sonics Ultrason, SU 31.2, pt.ii, 1984, ANSI-IEEE Std. 176, 1987  IEC TS Ed. 1.0 B 1CD, Piezoelectric and dielectric devices or requency control and selection - Glossary - Part 4-2: Piezoelectric materials - Piezoelectric ceramics, 1994  pren :2001, Piezoelectric properties o ceramic materials and components - Part 2: Methods o measurement and properties - Low power  pren :2001, Piezoelectric properties o ceramic materials and components - Part 3: Methods o measurement - High power  M. Musu-Coman, H. Ispas, M.I. Petrescu, E. Jianu, Improved retention o surace treated diamonds in sintered tools or processing ornamental stones, U.P.B. Sci. Bull., Series B, 68, No. 4, 47-56, 2006