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The elastic, piezoelectric, and dielectric properties of a 0.955Pb(Zn/sub 1/3/Nb/sub 2/3/)O/sub 3/-0.045PbTiO/sub 3/ (PZN-4.5%PT) multi-domain single crystal, poled along  of the original cubic direction, have been determined experimentally using combined resonance and ultrasonic methods. At room temperature, the PZN-4.5%PT single crystal has rhombohedral symmetry. After being poled along , four degenerate states still remain. Statistically, such a domain-engineered crystal may be treated as having an average tetragonal symmetry, and its material constants were determined based on 4 mm symmetry. It was confirmed that the electromechanical coupling coefficient k/sub 33/ for the domain-engineered samples is >90%, and the piezoelectric constant d/sub 33/ is >2000 pC/N. A soft shear mode with a velocity of 700 m/s was found in the  direction. From the measured experimental data, the orientational dependence of phase velocities and electromechanical coupling coefficients was calculated. The results showed that the transverse and longitudinal coupling coefficients, k/sub 31/ and k/sub 33/, reach their maximum along  and , respectively.