Nonlinear dynamics of the Frenkel-Kontorova model

The absence of a phase transformation involving substantial structural rearrangements and large volume changes is generally considered to be a key characteristic underpinning the high-rate capability of any battery electrode material. In apparent contradiction, nanoparticulate LiFePO4, a commercially important cathode material, displays exceptionally high rates, whereas its lithium-composition phase diagram indicates that it should react via a kinetically limited, two-phase nucleation and growth process. Knowledge concerning the equilibrium phases is therefore insufficient, and direct investigation of the dynamic process is required. Using time-resolved in situ x-ray powder diffraction, we reveal the existence of a continuous metastable solid solution phase during rapid lithium extraction and insertion. This nonequilibrium facile phase transformation route provides a mechanism for realizing high-rate capability of electrode materials that operate via two-phase reactions.

https://science.sciencemag.org/content/sci/344/6191/1252817.full.pdf

Capturing metastable structures during high-rate cycling of LiFePO4 nanoparticle electrodes

Three-dimensional phase field model of proper martensitic transformation

The electromechanical coupling in ferroelectric materials is controlled by several coexisting structural phenomena which can include piezoelectric lattice strain, 180 degrees and non-180 degrees domain wall motion, and interphase boundary motion. The structural mechanisms that contribute to electromechanical coupling have not been readily measured in the past, particularly under the low-to-medium driving electric field amplitudes at which many piezoelectric materials are used. In this feature, results from in situ, high-energy, and time-resolved X-ray diffraction experiments are interpreted together with macroscopic piezoelectric coefficient measurements in order to better understand the contribution of these mechanisms to the electromechanical coupling of polycrystalline ferroelectric materials. The compositions investigated include 2 mol% La-doped PbZr0.60Ti0.40O3, 2 mol% La-doped PbZr0.52Ti0.48O3, 2 mol% La-doped PbZr0.40Ti0.60O3, undoped PbZr0.52Ti0.48O3, and 2 mol% Fe-doped PbZr0.47Ti0.53O3. In all compositions, a strong correlation is found between the field-amplitude-dependence of the macroscopic piezoelectric coefficient and the contribution of non-180 degrees domain wall motion determined from the diffraction data. The results show directly that the Rayleigh-like behavior of d(33) piezoelectric coefficient is predominantly due to a Rayleigh-like behavior of non-180 degrees domain wall motion. Furthermore, after separating contributions from lattice (atomic level) and domain wall motion (nanoscale level) to the measured macroscopic piezoelectric properties, we show that previously ignored intergranular interactions (microscopic level) account for a surprisingly large portion of the electromechanical coupling. These results demonstrate that electromechanical coupling in polycrystalline aggregates is substantially different from that observed in single crystalline materials. The construct of emergence is used to describe how averaged macrolevel phenomena are different from the material response observed in an isolated subcomponent of the material. Consequently, and due to its size-scale complexity, the description of grain-to-grain interactions is presently inaccessible in most ab initio and phenomenological approaches. Results presented here demonstrate the need to account for these interactions in order to completely describe macroscopic electromechanical properties of polycrystalline materials.

G. R. Barsch

Papers

Twin Boundaries in Ferroelastic Media without Interface Dislocations