Neodymium-doped Bi4Ti3O12 (BNT) films are evaluated for use as lead-free thin-film piezoelectrics in microelectromechanical systems. Bi4Ti3O12, Bi3.25La0.75Ti3O12, and Bi3.25Nd0.75Ti3O12 films were fabricated by chemical solution deposition on Pt/TiOx/SiO2/Si substrates. Nd substitution promoted random orientation with low (00l) diffraction peaks. The 1-μm-thick Bi3.25Nd0.75Ti3O12 film annealed at 750 °C exhibited a remanent polarization of 26 μC/cm2. Typical butterfly field-induced strain loops were obtained in the BNT film capacitors. The electrically induced strain is 8.4×10−4 under the bipolar driving field of 220 kV/cm. These results show that BNT is a promising candidate for use in lead-free thin-film piezoelectrics.

Ferroelectric (Bi,R) 4 Ti 3 O 12 [R: rare earth] thin films were synthesized by the chemical solution deposition (CSD) method. Heat treatment above 600 C was required for the fabrication of crystalline (Bi,R) 4 Ti 3 O 12 thin films of Bi-layered perovskite structure on Pt/TiO x /SiO 2 /Si substrates. The orientation of the films prepared at 750 C depended upon the kind of substituent rare earth ions. Bi 4:12 Ti 3 O 12 (BIT) and Bi 3:35 La 0:75 Ti 3 O 12 (BLT) thin films revealed (00l) preferred orientation. On the other hand, Bi 3:35 Nd 0:75 Ti 3 O 12 (BNT), Bi 3:35 Sm 0:75 Ti 3 O 12 (BST) and Bi 3:35 Gd 0:75 Ti 3 O 12 (BGT) thin films showed random orientation with strong (117) reflection. Synthesized (Bi,R) 4 Ti 3 O 12 films exhibited the typical ferroelectric behavior. The BNT thin film showed P r of 21.6 mC/cm 2 , which was higher than the values of the other rare earth-doped BIT thin films.

We introduce a novel variational approach for evaluating PTV image pairs and sequences in two and three dimensions. We combine a discrete non-differentiable particle matching term with a continuous regularization term. An advanced mathematical method guarantees convergence to a local minimum. The experimental evaluation shows that our variational method competes with three alternative approaches. We outline the potential of our method for further developments.

Neodymium-modified Bi 4 Ti 3 O 12 , (Bi,Nd) 4 Ti 3 O 12 (BNT) ferroelectric thin films have been prepared on Pt/TiO x /SiO 2 /Si substrates using metal-organic precursor solutions by the chemical solution deposition method. The BNT precursor films crystallized into the Bi layered perovskite Bi 4 Ti 3 O 12 (BIT) as a single-phase above 600 • C. The synthesized BNT films revealed a random orientation having a strong 117 reflection, whereas nonsubstituted BIT thin films exhibited a random orientation with strong 00l diffractions. Among Bi 4−x Nd x Ti 3 O 12 [x = 0.0, 0.5, 0.75, 1.0] thin films, Bi 3.25 Nd 0.75 Ti 3 O 12 thin films showed a well-saturated P-E hysteresis loop with the highest P r (22 µC/cm 2 ) and a low E c (69 kV/cm) at an applied voltage of 5 V. The Nd-substitution with the optimum amount for the Bi site in the BIT structure was effective not only for promoting the 117 preferred orientation but also for improving the microstructure and ferroelectric properties of the resultant films.

Nd-and Ge-codoped Bi 4 Ti 3 O 12 thin films have been fabricated by chemical solution deposition. The effects of Ge doping in (Bi,Nd) 4 Ti 3 O 12 on microstructural and ferroelectric properties were investigated for the development of low-temperature fabrication of ferroelectric Bi 4 Ti 3 O 12 -based thin films. Bi 3:35 Nd 0:75 Ti 3Àx Ge x O 12 [0 x 0:5] thin films were found to crystallize into the Bi 4 Ti 3 O 12 phase above 600 C without forming any second phase. The crystal orientation and surface morphology of the synthesized films strongly depended on the Ge content of Bi 3:35 Nd 0:75 Ti 3Àx Ge x O 12 . Among various compositions of Bi 3:35 Nd 0:75 Ti 3Àx Ge x O 12 , Bi 3:35 Nd 0:75 Ti 2:9 Ge 0:1 O 12 thin films showed excellent surface morphology and ferroelectricity regardless of the processing temperature. Furthermore, the doping of Ge below x ¼ 0:1 was found to be effective in improving the ferroelectric properties of the low-temperature-processed films. The P r values of Bi 3:35 Nd 0:75 Ti 3Àx Ge x O 12 thin films with the optimum Ge content prepared at 600 C were above 15 mC/cm 2 and equal to those of the films crystallized at 700 C. Ge x O 12 (BNTG x ) compositions [0 x 0:5] (with 3% excess Bi) were dissolved in