2,427 research outputs found

### Derived brackets and sh Leibniz algebras

We develop a general framework for the construction of various derived
brackets. We show that suitably deforming the differential of a graded Leibniz
algebra extends the derived bracket construction and leads to the notion of
strong homotopy (sh) Leibniz algebra. We discuss the connections among homotopy
algebra theory, deformation theory and derived brackets. We prove that the
derived bracket construction induces a map from suitably defined deformation
theory equivalence classes to the isomorphism classes of sh Leibniz algebras.Comment: The Final Versio

### Positive effective Q12 electrostrictive coefficient in perovskites

It is demonstrated that for classical perovskites such as BaTiO3, SrTiO3 and
PbTiO3 electrostrictive strain induced by an electric field may not obey
traditionally considered "extension along the field, contraction perpendicular
to it" behavior if a sample is cut obliquely to the cubic crystallographic
directions

### Pressure-Induced Anomalous Phase Transitions and Colossal Enhancement of Piezoelectricity in PbTiO$_3$

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase
transition sequence induced by pressure, and a morphotropic phase boundary in a
pure compound using first-principles calculations. Huge dielectric and
piezoelectric coupling constants occur in the transition regions, comparable to
those observed in the new complex single-crystal solid-solution piezoelectrics
such as Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-PbTiO$_{3}$, which are expected to
revolutionize electromechanical applications. Our results show that
morphotropic phase boundaries and giant piezoelectric effects do not require
intrinsic disorder, and open the possibility of studying this effect in simple
systems.Comment: 4 pages, to appear in Phys. Rev. Let

### Optimal configuration of microstructure in ferroelectric materials by stochastic optimization

An optimization procedure determining the ideal configuration at the
microstructural level of ferroelectric (FE) materials is applied to maximize
piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from
that of single crystals because of the presence of crystallites (grains)
possessing crystallographic axes aligned imperfectly. The piezoelectric
properties of a polycrystalline (ceramic) FE is inextricably related to the
grain orientation distribution (texture). The set of combination of variables,
known as solution space, which dictates the texture of a ceramic is unlimited
and hence the choice of the optimal solution which maximizes the
piezoelectricity is complicated. Thus a stochastic global optimization combined
with homogenization is employed for the identification of the optimal granular
configuration of the FE ceramic microstructure with optimum piezoelectric
properties. The macroscopic equilibrium piezoelectric properties of
polycrystalline FE is calculated using mathematical homogenization at each
iteration step. The configuration of grains characterised by its orientations
at each iteration is generated using a randomly selected set of orientation
distribution parameters. Apparent enhancement of piezoelectric coefficient
$d_{33}$ is observed in an optimally oriented BaTiO$_3$ single crystal. A
configuration of crystallites, simultaneously constraining the orientation
distribution of the c-axis (polar axis) while incorporating ab-plane
randomness, which would multiply the overall piezoelectricity in ceramic
BaTiO$_{3}$ is also identified. The orientation distribution of the c-axes is
found to be a narrow Gaussian distribution centred around ${45^\circ}$. The
piezoelectric coefficient in such a ceramic is found to be nearly three times
as that of the single crystal.Comment: 11 pages, 7 figure

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