Acoustic properties of lead- based relaxor ferroelectric single crystals studied by micro- Brillouin scattering Jae-Hyeon Ko 1 *, Do Han Kim 1 , Seiji Kojima 1 , S. G. Lushnikov 2 and Guo-Zuang Ye 3 1 Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki, Japan 2 Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia 3 Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Outline � Introduction to relaxor ferroelectrics � Experimental Details - tandem Fabry-Perot interferometer(FPI) combined with a microscope � Experimental results and discussion - complex dielectric constant of PMT - Brillouin data of PZN-4.5% and 9%PT - Brillouin data of PMT � Conclusions
I. What is relaxor ferroelectrics? � Diffused, rounded and frequency-dependent dielectric constant (high dielectric constant near room temperature) � Existence of nanopolar clusters at high temperatures � No macroscopic change of the symmetry in many compounds � Dipolar glass model / random field model PbMg 1/3 Nb 2/3 O 3
Examples of Ferroelectric Relaxors � Complex Perovskites B-site complex Lead magnesium/zinc niobate PbMg 1/3 Nb 2/3 O 3 , PbZn 1/3 Nb 2/3 O 3 Lead scandium/magnesium tantalate PbSc 1/2 Ta 1/2 O 3 , PbMg 1/2 Ta 1/2 O 3 (cf: BaMg 1/2 Ta 1/2 O 3 ) A-site complex Lead lanthanum zirconate titanate (Pb 1-x La x )(Zr y Ti 1-y )O 3 (PLZT100(x/y/1-y)) � Tungsten bronze structure compositions Strontium barium niobate Sr 1-X Ba X Nb 2 O 6
Complex perovskite relaxors � Relaxor-based complex perovskite ferroelectrics: � Pb[(Zn 1/3 Nb 2/3 ) 1-x Ti x ]O 3 (PZN-x%PT) PZN-4.5%PT � Pb[(Mg 1/3 Nb 2/3 ) 1-x Ti x ]O 3 (PMN-x%PT) � outstanding piezoelectric properties when the electric field is along non-polar direction like [001] - strain level ~ 1.7 % - electromechanical coupling constant > 90% � promising materials for electromechanical applications like actuators, transducers… � superior to PZT due to the single crystal form
II. Experimental Details: Tandem multi-pass Fabry-Perot interferometer 1. The conventional scanning-type tandem multipass Fabry-Perot Interferometer is characterized by high contrast and resolution. 2. The combination of tandem FPI and a microscope made it possible to examine elastic properties of very small samples whose sizes are only a few microns.
III. Results (1) – complex dielectric constant of PMT and BMT (a) 6000 PMT 10 Hz 4000 ε ' • Typical dielectric dispersion in both real 2000 and imaginary part of the dielectric constant 1 MHz • Vogel-Fulcher relation from the maximum 21 (10 kHz ~ 1 MHz) BMT of ε ’ (ν) 20 − − ν = ν − 1 1 exp[ E k / ( T T )] 750 (b) o B max f PMT 600 1 MHz with T f = 124 K ε " 450 E/k B = 1250 K BMT 300 ν 0 =1.6 x 10 12 Hz (10 kHz ~ 1 MHz) 150 10 Hz 0 0 50 100 150 200 250 300 Temperature (K)
� Does the existence of T f indicate real freezing in the relaxation dynamics of relaxor ferroelectrics? * A.K. Tagantsev, PRL 72, 1100 (1994) τ g ( ) ∫ ε − ε = ε − ε τ * ( ) d (ln ) ∞ ∞ + ϖτ 0 1 i It is necessary to check the temperature dependence of the maximum relaxation time in the spectrum g( τ ) in order to find whether there is a real freezing or not.
III. Results (2) – Brillouin data of PZN-4.5% and 9%PT PZN-4.5%PT PZN-9%PT 46 43 cooling Cooling 45 heating Heating Brillouin Shift (GHz) Frequency (GHz) 42 44 43 41 42 40 41 0 200 400 600 800 300 350 400 450 500 550 Temperature (K) Temperature (K) • Clear hysteresis can be seen from the Brillouin shift measured during heating and cooling in both components. • It may indicate complex dynamics related to the formation of microdomains and glassy dynamics at low temperatures in case of PZN-4.5%PT and first- order character of the successive phase transitions in case of PZN-9%PT .
III. Results (3) – Brillouin and dielectric data of PMT for extracting τ max (T) 46 τ max (T=650K) ~ 1/2 π (45GHz) ~ 3.5 x 10 -12 s P M T 45 Brillouin Shift (GHz) τ max (T=205K) ~ 1/2 π (100kHz) 44 ~ 1.6 x 10 -6 s 43 B M T 42 T B (a) 6000 PMT 41 0 100 200 300 400 500 600 700 800 900 1000 Temperature (K) 10 Hz 4000 ε ' 2000 1 MHz • The onset of the dielectric and acoustic dispersion gives us the 21 BMT (10 kHz ~ 1 MHz) temperature dependence of τ max . 20 0 50 100 150 200 250 300 Temperature (K)
Two assumptions for the analysis of τ max (1) A single relaxation time distribution g (τ) contributes to both dielectric and acoustic dispersions. (2) The softening of Brillouin shift starts when the leading edge τ max of g (τ) becomes comparable to the time scale of the acoustic frequency of the longitudinal acoustic mode on cooling. g (τ,Τ) T 1 T 2 < T 1 T f ~T 3 < T 1 ln τ max (T 2 ) ln τ min ln τ
Temperature dependences of characteristic relaxation frequency ν (T max ) and maximum relaxation time τ max 6 − − ν = ν − (a) 1 1 exp[ E k / ( T T )] o B max f log ( ν (T max )) (Hz) 4 ± with T f = 124 2 K E/k B = 1250 K 2 ν 0 =1.6 x 10 12 Hz 0 4.8 5.2 5.6 6.0 -1 ) 1000/T (K 12 − τ = πν − 1 (2 ) exp[ E k / ( T T )] (b) 10 -1 ) (Hz) max 0 B f 8 ± with T f = 119 6 K log ((2 πτ max ) 6 E/k B = 1310 K ν 0 =5.5 x 10 11 Hz 4 2 0 1 2 3 4 5 6 -1 ) 1000/T (K
Comparison of PMT with other relaxor ferroelectrics PMT: this work PMN, PST: A.E.Glazounov, APL 73, 856 (1998) PLZT: S. Kamba, J. Phys.: Condens. Matter 12, 497 (2000) • In four kinds of relaxor ferroelectric single crystal, the temperature dependence of τ max followed the Vogel-Fulcher law with the same freezing temperature as that obtained from the frequency dependence of the temperature of dielectric maximum. • It may serve as a direct evidence for the real freezing of the relaxation time spectrum of PMT and other relaxor ferroelectrics.
Conclusions The temperature dependence of the maximum relaxation time, 1. τ max , in the spectrum g (τ) showed that there is a real freezing of the relaxation time distribution at a finite temperature ~120 K in PMT relaxor single crystal. The freezing process is described by the Vogel-Fulcher law for 2. τ max with the same freezing temperature obtained from the maximum dielectric constant. Brillouin scattering can be used to extend the frequency range for 3. obtaining information of relaxation dynamics of relaxor ferroelectrics up to GHz range. * Please refer to “E-08-P” presented by Mr. Do Han Kim regarding Brillouin study on PZN-9%PT.
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