As the grain size decreases to the nanometer range, the characteristics of the ferroelectric nanoceramic can be ultimately determined by the competition between two effects: the intrinsic effect that is associated with the local properties of the grain boundary and the extrinsic effect that arises from the dynamics of domain structure which is highly influenced by the depolarization field caused by the grain boundary. In this work we investigate such a competition with a phase-field simulation based on the time-dependent Ginzburg-Landau (TDGL) kinetic equation.The study is performed on poled/unpoled nanoceramics under high-and low-amplitude bipolar alternating electric field with selected grain size and loading frequency. Our calculations for poled BaTiO 3 at 100 Hz show that, for the grain size from 170 to 50 nm, its properties are dominated by the extrinsic effect, and from 50 to 10 nm, they are dominated by the intrinsic one. As the grain size decreases, the dielectric and piezoelectric constants at the remnant state continuously rise in the extrinsic-dominated region and then drop sharply in the intrinsic-dominated region. Our frequency calculations from 10 to 2,500 Hz at the grain size of 100 nm indicate that the high-frequency behavior is very similar to that of the small grain-size, intrinsic-dominated one, whereas the low-frequency behavior is closely related to that of the large grain-size, extrinsic-dominated part, with the demarcation line occurring around 400 Hz. For the un-poled ceramics under small signal loading, the intrinsic effect is dominant over the entire range of grain size and frequency.
For polycrystalline Beryllium (Be) specimens, data of yield strength, ultimate strength, elastic modulus, inelastic secant modulus elongation and grain size were obtained by using of material testing machine and metaloscope. It showed that: elastic modulus, inelastic secant modulus were basically independent with grain size; ultimate strength appeared at the end of tension process; relation between rate of yield strength to ultimate strength and elongation was found to be linear, but this rate had no clear correlation with grain size; relation between strength (yield, ultimate) and grain size was satisfied with Hall-Petch equation. Based on test data and analysis above, a bilinear model was given to simulate stress-strain constitutive behavior; an equation expressing relation between elongation and grain size was also derived.
A physics model was established for describing the particle size distribution of beryllium (Be) powder produced by impact attrition milling. In this model, two factors were considered: the first, the distribution of existing state of particles with different original kinetic energy should obey the Maxwell-Boltzmann statistics after impacted, it was that, being at higher energy level made big particles unstable, which were easy to be fractured into smaller pieces in impact attrition process, this influencing factor described as the negative exponential of particles size; the second, the tendency to remain low surface energy needed particles should keep big volume as much as possible, this effect defined as the cube of particles size. The actual particle size distribution of Be powder was resulted from the competition between these two factors. Calculating result from the model was in good agreement with data from measurement.
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