First Principles Calculations of Ionic Vibrational Frequencies in PbMg1/3Nb2/3O3

Lattice dynamics for several ordered supercells with composition PbMg1/3Nb2/3O (PMN) were calculated with first-principles frozen phonon methods. Nominal symmetries of the supercells studied are reduced by lattice instabilities. Lattice modes corresponding to these instabilities, equilibrium ionic positions, and infrared (IR) reflectivity spectra are reported.Comment: 6 pages; Fundamental physics of Ferroelectrics 200

Lattice dynamics of BaTiO3, PbTiO3 and PbZrO3: a comparative first-principles study

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.Comment: 9 pages, 2 figures (one in colors), revised version (small changes essentially in Sec. III

Clusters, phason elasticity, and entropic stabilisation: a theory perspective

Personal comments are made about the title subjects, including: the relation of Friedel oscillations to Hume-Rothery stabilisation; how calculations may resolve the random-tiling versus ideal pictures of quasicrystals; and the role of entropies apart from tile-configurational.Comment: IOP macros; 8pp, 1 figure. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

Enhancement of piezoelectricity in a mixed ferroelectric

We use first-principles density-functional total energy and polarization calculations to calculate the piezoelectric tensor at zero temperature for both cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest piezoelectric coefficient for the tetragonal configuration is enhanced by a factor of about three with respect to that of the cubic configuration. This can be attributed to both the larger strain-induced motion of cations relative to anions and higher Born effective charges in the tetragonal case. A normal mode decomposition shows that both cation ordering and local relaxation weaken the ferroelectric instability, enhancing piezoelectricity.Comment: 5 pages, revtex, 2 eps figure

Diffusion of Point Defects in Two-Dimensional Colloidal Crystals

We report the first study of the dynamics of point defects, mono and di-vacancies, in a confined 2-D colloidal crystal in real space and time using digital video microscopy. The defects are introduced by manipulating individual particles with optical tweezers. The diffusion rates are measured to be $D_{mono}/a^{2}\cong3.27\pm0.03$Hz for mono-vacancies and $D_{di}/a^{2}\cong3.71\pm0.03$Hz for di-vacancies. The elementary diffusion processes are identified and it is found that the diffusion of di-vacancies is enhanced by a \textit{dislocation dissociation-recombination} mechanism. Furthermore, the defects do not follow a simple random walk but their hopping exhibits memory effects, due to the reduced symmetry (compared to the triangular lattice) of their stable configurations, and the slow relaxation rates of the lattice modes.Comment: 6 pages (REVTEX), 5 figures (PS

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

Building effective models from sparse but precise data

A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a model that underfits the data is generally used for this purpose. For arbitrarily precise data free from statistic noise, e.g. ab initio calculations, we argue that it is more appropriate to begin with a ensemble of models that overfit the data. Within a Bayesian framework, a most likely model can be defined that incorporates physical knowledge, provides error estimates for systems not included in the fit, and reproduces the original data exactly. We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3 solid solution.Comment: 10 pages, 3 figures, submitted to Physical Review Letter