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By G.M. Crean,M. Locatelli,J. McGilp

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CASTONGUAY and J. D. N. CHEEKE Department of Physics, University of Sherbrooke, Sherbrooke, Quebec J1K2RI (Canada) (Received May 30,1989) Abstract Acoustic lenses made of thin piezoelectric lead zirconate titanate (PZT) films fabricated by a chemical sol-gel process are presented. A fre­ quency range between 50 and 250 MHz has been achieved. PZT films have been successfully coated on substrates such as fused quartz and metals, flat and cylindrical surfaces, and substrates with a large coating area or length.

M. Reese, H. D. Knuth, T. P. 8 9 10 11 Emmons, J. F. Weller and D. S. Czaplak, Proc. , IEEE, New York, 1986, p. 715. C. K. Jen, C. J. Chung, G. -P. Monchalin, P. Langlois and J. F. Bussiere, J. Am. Ceram. Soc, 70 (1987) C256. B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 1, Wiley, New York, 1973. F. S. Hickernell, Proc. , IEEE, New York, 1988,417. C. K. Jen, P. Cielo, J. F. Bussiere, F. Nadeau and G. W. Farnell, Appl Phys. , 46 (1985) 241. This page is intentionally left blank 27 Mechanical Characterization by Acoustic Techniques of SiC Chemical-vapour-deposited Thin Films J.

As the phase can have values much larger than 2n for large propagation distances and the arctan function is periodic, it was necessary to add 2n where phase jumps occurred. The values for the attenuation a{(o) and phase velocity v (a>) can now be obtained from the generalized one-dimensional wave equation for plane waves: + 00 u{x, t)= j A{a>)exp{-i{a)t-kx)} do (3) — 00 where k is the complex-valued wavevector: k{cD) = -^- + ia{a)) (4) V((0) After substitution of eqn. (4) into eqn. (3), a{co) and v{a)) can be determined by Fourier analysis of the displacement u{x, t) observed at two differ­ ent positions x{ and x2, which gives the Fourier 35 amplitudes A(x, co) and phases uation is then given by a(co) = -\n{A{x2,a))lA{xua))} X2 X[ col The atten- 10 b -■-l 0 J (5) \ -10 and the phase velocity is v{w) = - co{x2-xl) {x2,a))-(j>{xua)) 1 _]_ 1 X 1 2 Time (us) (6) Fig.

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