Elastic, dielectric, and piezoelectric constant matrix elements of a “single crystalline’’ (SC) film of vinylidene fluoride trifluoroethylene copolymer, P(VDF/TrFE), in which the orthorhombic [001] and [110] axes of fully extended chain crystals are preferentially oriented parallel to the stretching axis and normal to the surface, respectively, were measured at temperatures ranging from 10 K to the Curie point (402–404 K) by using a piezoelectric resonance method. All of the electromechanical coupling factors (k31, k32, k33, k24, and k15) are larger than those of conventional lamellar crystalline films. Some of the matrix elements for a P(VDF/TrFE) single crystal are derived from the measured values of constant matrix elements for the SC film. Some features characteristic of the SC film are revealed. The SC film has a large Young’s modulus for the stretching direction (1/s11) (121 GPa at 10 K). The properties related to the molecular motions along the chain axis, such as 1/s11, shear stiffness constant c55, shear piezoelectric constant e15, etc., exhibit strong relaxations around 250 K. The origin of these relaxations in the crystalline phase is discussed.

Crystalline structures, surface morphology, and ferroelectric response in ultrathin film of vinylidene fluoride and trifluoroethylene copolymer

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This paper studies the energy harvesting characteristics of piezoelectric laminates consisting of barium titanate (BaTiO3) and copper (Cu) from room temperature to cryogenic/high temperatures both experimentally and numerically. First, the output voltages of the piezoelectric BaTiO3/Cu laminates were measured from room temperature to a cryogenic temperature (77 K). The output power was evaluated for various values of load resistance. The results showed that the maximum output power density is approximately 2240 nW cm−3. The output voltages of the BaTiO3/Cu laminates were also measured from room temperature to a higher temperature (333 K). To discuss the output voltages of the BaTiO3/Cu laminates due to temperature changes, phase field and finite element simulations were combined. A phase field model for grain growth was used to generate grain structures. The phase field model was then employed for BaTiO3 polycrystals, coupled with the time-dependent Ginzburg–Landau theory and the oxygen vacancies diffusion, to calculate the temperature-dependent piezoelectric coefficient and permittivity. Using these properties, the output voltages of the BaTiO3/Cu laminates from room temperature to both 77 K and 333 K were analyzed by three dimensional finite element methods, and the results are presented for several grain sizes and oxygen vacancy densities. It was found that electricity in the BaTiO3 ceramic layer is generated not only through the piezoelectric effect caused by a thermally induced bending stress but also by the temperature dependence of the BaTiO3 piezoelectric coefficient and permittivity.

Shear piezoelectric properties of a vinylidene fluoride trifluoroethylene copolymer [P(VDF/TrFE)] have been studied in a temperature range from 10 to 350 K. The shear electromechanical coupling factors k15 and k24 at 290 K are found to be 0.19 and 0.20, respectively, the values being largest among the piezoelectric polymers known at present. The factors k15 and k24 remain constant below 200 K, while k24 increases and k15 decreases above 200 K. The effectiveness of P(VDF/TrFE) as a transverse ultrasonic transducer material was demonstrated by measurements of transverse sound velocities and absorptions in aluminum and poly(methyl methacrylate) with P(VDF/TrFE) shear transducers.

Frequency and impulse response characteristics of multilayered ultrasonic transducers comprising forward films of vinylidene fluoride and trifluoroethylene copolymer (P(VDF-TrFE)) and backward ferroelectric ceramic plates of lead-zirconate-titanate (PZT) and a backing load, are studied both theoretically and experimentally. These transducers can be driven in three operation modes: (1) P(VDF-TrFE) as a transmitter and a receiver, (2) PZT as a transmitter and a receiver, and (3) PZT as a transmitter and P(VDF-TrFE) as a receiver. It is found that, owing to the great difference in their acoustic and dielectric properties, PZT plates and P(VDF-TrFE) films operate independently at different frequencies, and that, in operation mode (3), the multilayered transducers exhibit broad frequency bandwidth or shorter impulse response characteristics with high sensitivity and high S/N ratio.

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Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.